/sci/ - Science & Math

[Anonymous No.15066203]

I completed a math minor as part of my CS degree and I still don’t know what “imaginary/complex” numbers are. I can memorise Euler’s formula, convert between rectangular and polar coordinates, pretend it’s some weird extension of the number line etc. But when I see an expression with an imaginary part, I don’t actually know what the fuck that means. I’ve watched tons of videos on it as well and I still don’t get it. When I learnt it I was just memorising gibberish as far as I was concerned.

[Anonymous No.15066209]

>>15066203
They're 2D vectors.

[Anonymous No.15066213]

>>15066209
That’s just the 2d number line bull shit again, I don’t get it.

[Anonymous No.15066219]

>>15066213
They're 2D numbers. You can do arithmetic with them. What don't you get?

[Anonymous No.15066224]

>>15066203
It's a spinny bit

[Anonymous No.15066226]

>>15066219
They mean nothing to me. The number “140” or the expression “9x + y” has meaning (if x and y are reals).

[Anonymous No.15066229]

>>15066226
>They mean nothing to me
Maybe you should have studied sociology or something. You still haven't clarified what aspect of them confuses you.

[Anonymous No.15066236]

>>15066229
Real numbers make sense because they have a tangible value. This includes negative numbers, because I understand in theory if I have 0 dollars and I give someone 1000 dollars I would have -1000 dollars (even though that’s not possible). Same doesn’t apply to imaginary numbers.

[Anonymous No.15066241]

>>15066203
You are simply thinking about it too hard.
[math] i [/math] is simply defined to be the solution to: [math] x^2 + 1 = 0 [/math]. Initially it was just a trick to solve cubic equations (see https://youtu.be/cUzklzVXJwo)) but it turns out they have some very nice properties; to be more specific, they form a [math] \textit{field} [/math], which basically means they share a lot of properties with standard real numbers and don't behave weirdly unlike a number system which say, would have a solution to [math] 0 x = 1 [/math]. This is why we define a solution to the former but not to the latter (except in special cases, see Riemann sphere). In application, complex numbers often reduce a problem to a very easy one (see for example, fast fourier transform). There's not much else to it.
The whole graph thing is just a visualisation but one way to think about it is that: in a number line multiplying by [math] -1 [/math] is essentially rotating 180 degrees, so multiplying by [math] i [/math] should be rotating by 90 degrees since [math] i^2 = -1 [/math]

[Anonymous No.15066248]

>>15066236
>a 2D vector isn't "tangible" enough for me
Are you retarded?

>in theory if I have 0 dollars and I give someone 1000 dollars I would have -1000 dollars
Ok, now I'm sure you are retarded.

[Anonymous No.15066254]

>>15066241
Nah, that doesn’t make sense. No value can be multiplied by itself to get less than 0. You can’t just define it to be x^2 + 1 = 0 because it’s “helpful”. Also how can you ROTATE anything that is one dimensional? Still don’t understand.

[Anonymous No.15066257]

>>15066254
>No value can be multiplied by itself to get less than 0
>less than 0
Complex numbers are not ordered.

>how can you ROTATE anything that is one dimensional?
Complex numbers are two-dimensional. You do not have a CS degree. You're a highschool dropout.

[Anonymous No.15066259]

Consider a geometrical vector in a plane. You can divide it by another geometric vector parallel to it and get a number.

Now if you rotate the divisor vector 90 degrees and try the same thing, what do you think you'll get?

[Anonymous No.15066261]

>>15066257
> Complex numbers are not ordered
Exactly why it doesn’t make sense, has no tangible value
> Complex numbers are two-dimensional. You do not have a CS degree. You're a highschool dropout.
He said you can rotate 1 180 degrees to get -1

[Anonymous No.15066265]

>>15066261
>I just can't wrap my head around a 2D vector
>It's not tangible!!!!
LOL.

>He said you can rotate 1 180 degrees to get -1
Yes. What's the problem here?

[Anonymous No.15066267]

>>15066259
>divide a vector by a vector
Doesn’t make sense, can only divide by a real number.

[Anonymous No.15066273]

>>15066265
In order to rotate something that is 1 dimensional you would have to move it into 2 dimensions. Im sure you can see the problem with that.

[Anonymous No.15066276]

>>15066273
>In order to rotate something that is 1 dimensional
Have you taken your meds today? He's talking about rotating something 2-dimensional.

[Anonymous No.15066281]

>>15066203
How many people who go to college have this experience?

[Anonymous No.15066285]

>>15066276
1 is 1 dimensional

[Anonymous No.15066288]

>>15066285
Not in this context. Here's something I don't understand: you are stupid and you know it. You need help from people smarter than you and you know it. Considering this, why are you so aggressive about your stupidity? Why do you keep asserting your stupidity as if you were in the right about anything?

[Anonymous No.15066290]

>>15066288
You’re wrong and I’m right. Simple.

[Anonymous No.15066291]

>>15066290
This is what mental illness looks like. The sad thing is that 80% of this board is like you.

[Anonymous No.15066295]

>>15066254
>No value can be multiplied by itself to get less than 0.
That's according to you. Nothing in math says that. There is another system of numbers called integers modulo, in which you can keep adding 1 to itself until it results in 0.
>You can’t just define it to be x^2 + 1 = 0 because it’s “helpful”.
That's literally why things are defined. 0! is defined to be 1 because it is helpful, and also why 1 is not defined to be prime.
There is no one dimensional line in the universe yet we study geometry. Neither are there any irrational numbers, yet you seem to have no problem with that. It's preconceptions like these about what should or should not be is what held back math for centuries. We invent math not the other way, math cannot tell us what should we do.

[Anonymous No.15066317]

>>15066295
Well if you’re admitting that it’s just making shit up, then I have equal right to say you can’t define it like that.

[Anonymous No.15066337]

>>15066317
>you can’t define it like that.
But I did?

[Anonymous No.15066342]

>>15066337
You heckin' can't because it makes no sense. I want you stupid brainlets to explain it in terms of something that makes sense. For example, if I give you 1000 dollars I have -$1000. See, negative numbers make sense. I can visualize the value of -1000 unlike your schizo complex shit.

[Anonymous No.15066351]

>>15066342
I can because it forms a consistent system that has wide applications. If you can't make sense out of it, that's your problem. What sense is there in irrational numbers?

[Anonymous No.15066358]

>>15066351
Wow. You people are dumb. I don't care how "consistent" your "system" is. It makes no sense and means nothing to me. If it's valid, why doesn't it make sense?

[Anonymous No.15066378]

>>15066295
>There is no one dimensional line in the universe yet we study geometry. Neither are there any irrational numbers, yet you seem to have no problem with that.
Do you have even a single fact to back that up?

[Anonymous No.15066387]

>>15066267
Why doesn't it make sense? If 2u = 3v then u/v = 3/2. I haven't gotten to the complex number part yet, humor me.

[Anonymous No.15066392]

>>15066387
Not OP but you sound retarded also. What you did only makes sense if the vectors happen to be collinear.

[Anonymous No.15066395]

>>15066337
I just said you can’t though ? Can’t you provide a logical argument for your definition? My argument that there are no numbers that can be multiplied to equal less than 0 is more logical so I say it’s correct. How’s being “helpful” better than being logical?
>>15066351
There isn’t any sense in irrational numbers, but I partly understand because I just pretend they’re rational numbers. I simply don’t understand what complex numbers are and I guess you’re saying that no one does? Because you have not been able to concretely logically explain it.

[Anonymous No.15066401]

I guess you could try to understand it in terms of bi vectors

[Anonymous No.15066478]

>>15066392
Obviously. a - b only makes sense if b <= a. a/b only makes sense if b fits into a.

[Anonymous No.15066486]

>>15066478
The levels of delusion on this board are simply off the charts.

[Anonymous No.15066555]

>>15066395
>Because you have not been able to concretely logically explain it.
Oh you want a logical definition? Then why didn't you say that first, anon. How silly of me! Okay here goes.

Assume ZFC holds.

Then define [math] \mathbb N = \{0,1, \dots \}[/math] to be the following:
[math] 0 = \emptyset\\ 1 = 0 \cup \{ 0 \} \\ n + 1 = n \cup \{ n \} [/math]
where [math] n + 1 [/math] is the number after [math] n [/math].
Define [math] S : \mathbb N \to \mathbb N, n \mapsto (n+1) [/math].
Define [math] + : \mathbb N \times \mathbb N \to \mathbb N [/math] to be a binary operation such that: [math] a + 0 = a, a + S(b) = S(a+b)[/math].
Define [math] \times : \mathbb N \times \mathbb N \to \mathbb N [/math] to be a binary operation such that: [math] a \times 0 = 0, a \times S(b) = (a \times b) + a [/math].
We call the set [math] \mathbb N [/math] along with the operations [math] +, \times [/math] the semiring of natural numbers.

Define [math] \mathbb Z [/math] as an equivalence class of pair of natural numbers the following way:
[math] (a, b) \sim (c,d) \iff a + d = b + c[/math]
Using [math] [(a,b)] [/math] to denote the equivalence class containing [math] (a,b) [/math], we define addition and multiplication as:
[math] [(a,b)] + [(c,d)] := [(a+c, b+d)] \\
[(a,b)] \times [(c,d)] := [(ac+bd, ad+bc)] [/math]
We call the set [math] \mathbb Z [/math] along with the operations [math] +, \times [/math] the ring of integers.

Define [math] \mathbb Q [/math] to be an equivalence class of pairs of an integer and a non-zero integer the following way:
[math] (a, b) \sim (c,d) \iff ad = bc [/math]
Addition and multiplication is defined as follows:
[math] [(a,b)] + [(c,d)] := [(ad + bc , bd)] \\
[(a,b)] \times [(c,d)] := [(ab, cd)] [/math]
We call the set [math] \mathbb Q [/math] along with the operations [math] +, \times [/math] the field of rationals.

cont.

[Anonymous No.15066557]

>>15066358
>It makes no sense and means nothing to me
Math is not built around what makes sense to you

>>15066395
>>15066555
A subset [math] A [/math] of the rational numbers is called a cut if it possesses the following three properties:
[eqn] A \neq \emptyset \land A \neq \mathbb Q \\
r \in A \implies A \includes \{q \in \mathbb Q : q < r \} \\
r \in A \implies \exists s \in A \; r < s [/eqn]
Define [math] \mathbb R [/math] to be the set of all cuts in [math] \mathbb Q[/math]. Given [math] A, B \in \mathbb R[/math] define addition and multiplication in the following manner:
[eqn] A + B = \{ a + b : a \in A \land b \in B \} \\
A \times B = \{ a b : a \in A, b \in B, a, b \geq 0} \cup {q \in Q : q < 0} \impliedby A,B \includes \{ p \in Q : p < 0 \}
[/eqn]
We call the set [math] \mathbb R [/math] along with the operations [math] +, \times [/math] the field of reals.

Define [math] \mathbb C [/math] to be the set of pairs of members of [math] \mathbb R [/math].
Addition and multiplication is defined as follows:
[eqn]
(a,b) + (c,d) = (a+c,b+d) \\
(a,b) \times (c,d) = (ac − bd, ad + bc)
[/eqn]

There! Hope that helps anon.

[Anonymous No.15066561]

>>15066358
>It makes no sense and means nothing to me
Math is not built around what makes sense to you

>>15066395
>>15066555
A subset [math] A [/math] of the rational numbers is called a cut if it possesses the following three properties:
[eqn] A \neq \emptyset \land A \neq \mathbb Q \\
r \in A \implies A \subseteq \{q \in \mathbb Q : q < r \} \\
r \in A \implies \exists s \in A \; r < s [/eqn]
Define [math] \mathbb R [/math] to be the set of all cuts in [math] \mathbb Q[/math]. Given [math] A, B \in \mathbb R[/math] define addition and multiplication in the following manner:
[eqn] A + B = \{ a + b : a \in A \land b \in B \} \\
A \times B = \{ a b : a \in A, b \in B, a, b \geq 0 \} \cup {q \in Q : q < 0}
[/eqn]
We call the set [math] \mathbb R [/math] along with the operations [math] +, \times [/math] the field of reals.

Define [math] \mathbb C [/math] to be the set of pairs of members of [math] \mathbb R [/math].
Addition and multiplication is defined as follows:
[eqn]
(a,b) + (c,d) = (a+c,b+d) \\
(a,b) \times (c,d) = (ac − bd, ad + bc)
[/eqn]

There! Hope that helps anon.

[Anonymous No.15066562]

>>15066358
>retard can't into definitions
many such cases

[Anonymous No.15066582]

>>15066561
>You have not able to logically EXPLAIN it
>posts definition copypasted from internet
That’s not a logical explanation for WHY complex numbers should be allowed to be used.

[Anonymous No.15066588]

>>15066582
>That’s not a logical explanation for WHY complex numbers should be allowed to be used.
Because it is helpful.

[Anonymous No.15066589]

>>15066562
I'm not a retard. I have a fucking CS degree. You math retards and your complex religion are the problem ITT.

[Anonymous No.15066591]

>>15066588
How can it be helpful if it means nothing to me? Explain it in terms that make sense. For example, if I give you 1000 dollars, I have -$1000. -1000 is a tangible value. You retards don't understand what "tangible" means.

[Anonymous No.15066600]

>>15066589
Wait until you hear about geometric algebra ohh boy CS fags are so not smart as they think they are

[Anonymous No.15066608]

>>15066600
I'm an expert in AI. I have a degree in Python programming. You're a fucking nobody. We will replace mathematicians in two more weeks.

[Anonymous No.15066616]

>>15066591
Explain [math] \sqrt 2 [/math] in tangible terms

[Anonymous No.15066620]

>>15066236
>Real numbers make sense because they have a tangible value
Give me pi apples

[Anonymous No.15066624]

>>15066591
You said logical. I gave you a logical definition. Now you want a tangible example. What the fuck do you want? Make up your mind.
>For example, if I give you 1000 dollars, I have -$1000. -1000 is a tangible value
How is that tangible when it is literally untrue? If you give me 1000 you have your 1000 subtracted from your bank balance which must be nonnegative. You are deciding what's tangible and what's not at your whim, but a number system which trivialises several problems in Mathematics (and Physics and Computer Science) is where you draw the line?

[Anonymous No.15066626]

>>15066624
>How is that tangible
Because -1000 dollars is something tangible that makes sense to me, unlike your schizo complex numbers. Wow. Mathfags are really stupid.

[Anonymous No.15066636]

A couplet of numberd associated with few arithmetic laws. As complex numbers do not exist in nature, they are just a mathematical trick
>>15066209
We already have 2d vector and this aint them, imbesil. Stop retarding things to the point they arent the thing.

[Anonymous No.15066638]

>>15066591
-$1000 is an operation not a value. An actual tangible example would be debt, which is literally the opposite of your example where someone gives you money. The fact you could not figure this out is sad. That in itself warrants complex numbers. Also you want a tangible example to complex number. Fine. The Schrodinger wave equation:
[math] i \hbar \frac{d}{dt} \left \vert \Psi (t) \right \rangle = \hat{H} \left \vert \Psi (t) \right \rangle [/math]
This is Physics. It is more tangible than your non-example.

[Anonymous No.15066640]

>>15066636
>We already have 2d vector and this aint them
Prove it, mouth breather. Show how they are different.

[Anonymous No.15066643]

>>15066203
Math has nothing to do with real world. Everything in math is just what it formal definition is. Complex numbers and in general higher mathematics is not tangible, but unfortunately it has many real world applications to le hecking tangible problems, which attracts low iq people like (you) to make bait posts.

[Anonymous No.15066645]

>>15066620
I cannot. But I can give approximate value that’s close to it. Simple.

[Anonymous No.15066652]

>>15066591
If you multiply two vectors where the "y-coordinate" is represented as a multiple of i, and the x coordinate as a multiple of 1, its the same as adding the angles and multiplying the magnitudes. For example, (1 + i) * (2 - i) = (3 + i) when you multiply it out. You can draw out these three vectors and verify that (1 + i) has an angle of 45 degrees, (2 - i) has an angle of around -26 degrees, and (3 + i) has an angle of about 45 - 26 = 19 degrees.

If you still think this is still schizo shit, then ask yourself why multiplying a positive number by a negative number yields a negative number. This isn't really a tangible operation either, unless you consider 1 and -1 to be vectors following the same multiplication logic. The vector of 1 has an angle of 0, -1 has an angle of 180, multiply the two and you get a vector of angle 0 + 180 = 180. This would of course be -1. And if you multiply -1 by itself, you get a vector of angle 180 + 180 = 360 (or 0), which is 1 again. By the same token, multiply i (a vector that's 90 degrees with a magnitude of 1) by itself and you end up back with -1, since 90 + 90 = 180.

[Anonymous No.15066653]

>>15066652
Sorry, that's still not tangible.

[Anonymous No.15066656]

>>15066653
Is multiplying a positive by a negative not tangible to you?

[Anonymous No.15066657]

>>15066656
It's not the same. One makes sense to me and the other dozen.

[Anonymous No.15066662]

>>15066657
I don't see how multiplying a positive number by a negative number makes sense at all (or multiplying a negative by a negative for that matter) unless you think of the numbers as being vectors, where negatives point in the opposite direction, and multiplying essentially just adds the angles. And if you do think of it that way, then understanding imaginary numbers should be a piece of cake; just think of them as being at a 90 degree angle to the positives and negatives.

[Anonymous No.15066668]

>>15066662
I don't care what makes sense to you. My sense is the normal sense, you're just a math freak.

[Anonymous No.15066693]

>>15066662
I have no problem with treating numbers as 1 dimensional vectors, that makes sense. They still have tangible values. Two dimensional vectors do not.

[Anonymous No.15066751]

>>15066203
Consider the euclidean plane and draw a Cartesian coordinate system. Any point in space will hence have a pair of coodinates (x,y). We can construct an opperation on pairs of points in the plane by (x1,y1)*(x2,y2) = (x1*x2-y1*y2,x1*y2+x2*y1), this point turns out to be the point with distance from the origin equal to the product of the distance of the origin of the two original points, and makes the angle a + b with the x axis (counterclockwise) where a is the angle that (x1,y1) makes with the x-axis and b the angle (x2,y2) makes.
Now give (1,0) the name 1 and (0,1) the name i, you can check they satisfy the usual rules of algebra.

[Anonymous No.15066783]

>>15066589
>I have a fucking CS degree

[Anonymous No.15066869]

>>15066203
You are trying far too hard to associate mathematics directly with the physical word, rather than conceiving of mathematical objects for the sake of mathematics.

[Anonymous No.15066878]

>>15066869
Have to add that even in that, you're doing a terrible job.

[Anonymous No.15066887]

>be EE
>can easily see complex numbers in electrical circuits
OP is just low IQ.

[Anonymous No.15066928]

>>15066203
They are rotation + translation operators on the 2D plane.
Restricting the set of possible functions on 2 variables to a combination of these outputs additional properties for derivability and integration.

[Anonymous No.15066934]

>>15066254
No one said it is one dimensional.
The dimensionality is not determined by the number of characters you use to express your number.
You make two 90 degrees turn around the normal axis to your plane and you are at the same point you end up with if you just translated backwards.
You are a high-school dropout. Quit the larping.

[Anonymous No.15066941]

>>15066203
It doesn't make sense to you because you're retarded, that's all.

[Anonymous No.15066948]

>>15066941
Mathematicians are basically retarded philosophers who pull unnatural and nonscientific concepts like complex numbers out of their ass. Modern mathematics is worthless and plagued by the ideas of christcuck philosophers like Gödel and Cantor.

[Anonymous No.15067008]

>>15066645
close your eyes and imagine pi apples

[Anonymous No.15067012]

>>15067008
Imagination is retard cope for artists, which are the only thing lower than philosophers. AI is going to replace both in two more weeks.

[Anonymous No.15067035]

>>15066203
Kek, it's not just a meme, CS students really are fucking stupid.

[Anonymous No.15067055]

This bait was a slow boil.

[Anonymous No.15067066]

>>15066640
The manifestation of complex is certain subset of 2x2 real matrix' not 2x1 real vector. There

[Anonymous No.15067070]

>>15066638
Its fake physics, handwaving equation to get something result. Put enough complex variables, a some result must occur

[Anonymous No.15067083]

>>15067066
>not 2x1 real vector
Name one difference, retard. You literally can't. You will deflect again in your next post.

[Anonymous No.15067156]

OP is a math undergrad pretending to be a CS undergrad.
How do you fags not see this?

[Anonymous No.15067162]

>>15067156
Telling the difference between a troll and an actual retard isn't always a trivial task, especially since I've seen people unironically espouse these types of views.

[Anonymous No.15067166]

Maybe the real retards were the guys who fell for this bait thread

[Anonymous No.15067171]

>>15067166
Maybe the real retards were the frens we made along the way.

[Anonymous No.15067215]

>>15066203
they exist, so that we can solve equations like x^2 + 1 = 0; in other words, the complex numbers a algebraically "richer" than the real numbers and this is why they exist. The fundamental theorem of algebra wouldn't work without them.

[Anonymous No.15067255]

>>15067083
2x2 is not 2x1. Simple as

[Anonymous No.15068064]

>>15066668
Anon I commend you, this is some of the highest quality bait I've seen in quite a while.

[Anonymous No.15068085]

unironically op is right. most people in this thread seem to believe that they understand imaginary numbers but are just spouting the same bs. op was asking for the intuition behind a complex number, the intuition behind "rotating" complex numbers. not the definition or properties.

[Anonymous No.15068097]

>>15067215
The "solution" to that equation is just another imaginary (fake) number. Why would anyone, who is distrustful of imaginary numbers, be persuaded by this argument? Introduce fake numbers to get fake solutions to insoluble equations? So epic, I love science!

[Anonymous No.15068122]

>>15066591
Mohr your black ass one step forward. Make a half rotation around the normal axis to your plane passing through the origin. Move a step backward.
Figure out where you are and here you made use of complex numbers.
Dumb nigger.

[Anonymous No.15068853]

>>15066620
>>15067008

[Anonymous No.15069389]

>>15066203
forget about what literally everyone says here. if you want TANGIBLE then read up on complex numbers in terms of their magnitude and angle (Wikipedia complex numbers, polar complex plane). now you're just considering points in the plane and you have intuitive, geometric rules to "multiply" them (read: combine two to get a third).

[Anonymous No.15069509]

>>15066620

[Anonymous No.15069568]

>>15068085
>intuition
you're looking for psychology not math retard

[Anonymous No.15069752]

>>15066652
A positive times a negative isn't schizo. It's like saying I have 5 (positive) 1000 debts (negative) = $5000 debt. It makes sense.


What OP is looking for is a really simplistic, real-world understanding of imaginary numbers. Just give him the most basic example with relationship to real world events and he'll move on.

[Anonymous No.15070174]

>>15069568
its funny, a computer can replace you considering all you know are definitions and calculations.

[Anonymous No.15070273]

I like how the real numbers are like a dumbed down complex plane, and multiplying by -1 is like a 180 degree rotation.
> /sci/ should have math captchas, not this image matching right brain crapola

[Anonymous No.15070361]

>>15066291
No, the sad thing is that you probably actually think you have said anything helpful in this thread and don't understand that you come off more retarded than the person asking a simple question when you start slipping into low IQ fallacies like name calling and ad hominem.

[Anonymous No.15070366]

>>15066337
But he already defined you as someone who always defines things incorrectly, so its no surprise that you would try to define things in ways that can not actually be defined.

[Anonymous No.15070368]

>>15066561
So you agree that your answers are all illogical and don't matter since math isn't meant to make sense and anyone can just define whatever answer they want to any math question since there is no obligation in math to ensure the answer makes sense?

[Anonymous No.15070373]

>>15068122
Good luck trying to convert that movement into a complex number math equation since a movement of sqrt(-1) never actually occurs in your scenario.

[Anonymous No.15070435]

>>15066643
>Math has nothing to do with real world.
>it has many real world applications
Self contradicting posts will be ignored.

[Anonymous No.15070482]

>>15070435
>Self contradicting posts will be ignored.
>replies to a self contradicting post.
Self contradicting posts will be ignored.

[Anonymous No.15070499]

>>15070482
Will be is future tense, not past, if they said self contradicting posts have been ignored or are being ignored, you would have a case.

[Anonymous No.15070507]

>>15070361
>you probably actually think you have said anything helpful
I know I didn't. The braindead nigger (who is most likely you) wouldn't let any attempts to help him proceed in a productive manner. Someone was trying to explain to him why multiplying by i corresponds to a 90 degree rotation but the refuses to wrap his head around treating 1 as a vector. It's not that he can't understand per se. It's that his tiny, aggressive monkey mind refuses to consider it.

[Anonymous No.15070521]

>>15070507
>i corresponds to a 90 degree rotation
Because you couldn't explain what it is about square rooting that equivocates to rotation and you can't explain how rotating an apple 90 degrees somehow makes it imaginary, your explanation is vague and incomplete and you can't accept that it is the "teacher" that failed and got aggressive with name calling rather than the student asking the question and didn't understand the poor explanation that was provided.

[Anonymous No.15070525]

>>15070521
>you couldn't explain what it is about square rooting that equivocates to rotation
How can you explain this to braindead nigger who keeps insisting that it can't correspond to rotation because a vector aligned with the X axis 1D and not 2D? lol

[Anonymous No.15070532]

>>15070525
He keeps insisting because you keep failing to explain how the square root function is actually a rotation.

If you know you can't explain it and all that comes out of your foul mouth is nonsense, then why don't you just go back and let someone who thinks they can actually explain it give it a shot? kek

[Anonymous No.15070535]

>>15070532
How can you explain the correspondence to a rotation if the nigger refuses to acknowledge the premise that complex numbers are 2D, even if they happen to fall on the real axis?

[Anonymous No.15070543]

>>15070535
He didn't, he said that imaginary numbers are 1D and they are.
Imaginary numbers don't actually fall on the real axis (it is a function made of of real axis elements, but the result is not a real number) and you can't explain how the sqrt function is a rotation on the real axis for anything except imaginary numbers which you arbitrarily turn the orthogonal imaginary dimension 90 degrees from the real dimension to come up with a 2D complex plane without explaining how and why that is appropriate in any physical sense that OP can relate to. He knows how to rotate objects like apples in 3D just not into imaginary space.

[Anonymous No.15070546]

>>15070543
I knew you were that shameful nigger.

[Anonymous No.15070551]

>>15070546
Don't worry we both fully understand now that you devolve into brief pure outbursts of name calling that you can't provide any real physical example to express imaginary space and the complex plane.

[Anonymous No.15070574]

I have 1 Apple. Make sense.
I have -1 Apple. I owe 1 Apple. Make sense.
I have i Apple. ???????????????

[Anonymous No.15070593]

>>15066203
Damn I'm glad I'm studying EE instead of CS. I really don't want to be around such people.

[Anonymous No.15070600]

>>15070574
I can introspect on the root essence of Apple and know what it is for Apple to be and what needs to be squared away so that nature owes me Apple.

[Anonymous No.15070637]

>>15070551
At least you're no longer pretending to be a different poster. What a waste of life.

[Anonymous No.15070754]

>>15066203
imaginary numbers are the reason that we should scrap the schrodinger equation.

[Anonymous No.15070799]

>>15070637
You still haven't provided any physical real world corollary for imaginary space, no matter how much you try to project your own failure onto someone else.

[Anonymous No.15070818]

>>15070799
>You still haven't provided any physical real world corollary
Why do I need to provide one? If you're too much of a driveling imbecile to understand abstract concepts, even if they're babby-tier ones like 2D points and planes, why are you on this board?

[Anonymous No.15070824]

>>15070818
Why do you keep replying to the thread when you clearly don't know the answer to the question?
Do you really think anger outbursts at your own ignorance is a suitable replacement for being able to answer the question?
You still don't even understand or acknowledge that the imaginary domain is not 2D, so appealing to 2D has nothing to due with the question.

[Anonymous No.15070828]

>>15070824
>Why do you keep replying to the thread
Because I enjoy reminding you of your inferiority.

>you clearly don't know the answer to the question
What's the question, again? "It doesn't make heckin' sense" is not a question. "B-b-but what about my physical analogies" is not a question, either.

>the imaginary domain is not 2D
Complex numbers are 2D. Maybe once you wrap your tiny head around this fact, you can ask an actual question. lol

[Anonymous No.15070829]

>>15070824
Worthless imbecile just stop wasting this dude's time

[Anonymous No.15070836]

>>15070828
You are the one who can't seem to answer the question.

How much is a sqrt(-1) amount of things, we have seen what a pi number of apples is and what it is to owe apple, so post an image of i number of apples or explain how you can repay i number of apples to someone else.

>Complex numbers are 2D.
Imaginary numbers, OP clearly understands real components, it is only the imaginary components he is asking about and you are failing to properly explain.

[Anonymous No.15070840]

>>15070829
He is the one wasting time with worthless name calling and ad hominem rather than simply answering the question and explaining what an imaginary amount of something is,

[Anonymous No.15070843]

>>15070836
>How much is a sqrt(-1) amount of things
It isn't any "amount of things". Was that your question? I guess we've answered it and you can kill yourself now. lol

>OP clearly understands real components, it is only the imaginary components he is asking about
What are you asking about it?

[Anonymous No.15070847]

>x^2 + 1 = 0? That’s i of course, you idiot!
>1/0? Noooooooooooooo that doesn’t make any sense!!!!

[Anonymous No.15070851]

>>15070843
So there is no such thing as i number of things, i is an illogical nonsensical concept that isn't actually a number and doesn't actually exist?

>What are you asking about it?
I am asking about things well above your pay grade that you clearly don't understand and can't properly answer since you prefer nonsense answer like imaginary is just a 90 degree rotation of reality.

[Anonymous No.15070853]

>>15070851
>there is no such thing as i number of things
Yeah. Now you're getting it, retard.

>I am asking about things
What are those things? Can you formulate a coherent question, gigatard?

[Anonymous No.15070856]

>>15070853
No point asking you a coherent question when you have demonstrated time and time again that you possess a complete inability to provide coherent answers and don't understand the imaginary domain.

[Anonymous No.15070857]

>>15070856
>No point asking you a coherent question
How do you know? Have you tried it? Show me where ITT you have asked a coherent question. lol

[Anonymous No.15070861]

>>15070857
You just don’t understand because you’re dumb lol stupid idiot, I’m smarter than you ok? I know what i is and ur don’t it’s just a rotation and stuff so like why don’t you shut up

[Anonymous No.15070863]

>>15070857
Yes I asked you to demonstrate how an imaginary number is a number and you just complained about being retarded instead and basically claimed it was impossible on the grounds that an imaginary number is not a number. Total drivel and nonsense from a unterwit.

If you ever figure out how to demonstrate that an imaginary number is a number feel free to come back and screech some more about rotating reality by 90 degrees or whatever nonsense your slow brain comes up with.

[Anonymous No.15070864]

>>15070863
>demonstrate how an imaginary number is a number
You can do all the usual arithmetic operations on it in accordance with the field axioms, so it's a number.

[Anonymous No.15070867]

>>15066358
It's perfectly fine that it makes no sense to you. Do you speak Chinese? Arabic? There are many people to whom they make perfect sense. Your inability to understand is simply your lack of a particular skill or skills, not others being stupid or incorrect.

[Anonymous No.15070869]

>>15070864
Ok so explain how to divide 1 apple into i pieces.

[Anonymous No.15070871]

>>15070867
Shut up. If you were as smart as you think you are, you would have answered my coherent and intelligent questions in a productive matter, but all you can do is lash out.

[Anonymous No.15070875]

>>15070869
How can you divide 1 apple into -1 pieces? Either way, the one time you managed to ask a coherent question, it did get an answer. What's your complaint, gigatard?

[Anonymous No.15070881]

>>15070875
>How can you divide 1 apple into -1 pieces?
You sell it so that it is no longer 1 apple it is one apple removed from your inventory. Now do i.

> it did get an answer.
No you just asked a different question because you can't answer how to divide 1 apple into i pieces disproving your claim that every operation applies equally to i.

[Anonymous No.15070885]

>to divide an apple by -1 you sell it so that it is no longer 1 apple it is one apple removed from your inventory.
The final and ultimate state.

[Anonymous No.15070890]

>>15070871
I didn't make any claims about myself. I'm simply asking you to accept that in this case you are failing to understand something other people do understand and that your failure to understand says basically nothing about the concepts you fail to understand.

What I'm saying is simple and talking about it doesn't require either you or I to be smart or well educated.

Since you claim to not understand very well, it seems like you shouldn't have much trouble accepting what I'm saying.

From there you can try to learn more until you do understand it. Most of the hostility you're getting is because you are making strong claims about something you said you know little about. Other people will take you more seriously if you learn more about a topic before trying to convince others you understand it better than they do.

[Anonymous No.15070892]

>>15070890
I will never accept it because the things you say are nonsense and I've already disproved it. You can't divide an apple by i.

[Anonymous No.15070893]

>>15070885
Name calling is still not a suitable replacement for an actual answer, no matter how brief and thoughtless you make your insults.
I still don't understand why you feel the need to keep replying when you obviously don't understand the subject, but keep rotating reality by 90 degrees and maybe you will be able to explain your imagination properly one day.

[Anonymous No.15070897]

>to divide an apple by -1 you sell it so that it is no longer 1 apple it is one apple removed from your inventory.
>you obviously don't understand the subject, but keep rotating reality

[Anonymous No.15070899]

>>15070869
>Ok so explain how to divide 1 apple into i pieces.
You shove it up your ass i^2 times and then sell it.

[Anonymous No.15070900]

>>15070897
>I still can't reasonably explain how an imaginary number is a number, so I will project my anger about my own ignorance onto others.

[Anonymous No.15070901]

>>15070892
I don't think anything in my two posts was nonsense, but even if you read bad arguments in favor of something, that doesn't mean it's wrong and it really doesn't mean you should decide to live the rest of your life opposed to whatever people argue about poorly.

What if I gave you a nonsense argument in favor of breathing? Tuesdays are green, so you should breathe regularly.

[Anonymous No.15070902]

>to divide an apple by -1 you sell it so that it is no longer 1 apple it is one apple removed from your inventory.
>you obviously don't understand the subject

[Anonymous No.15070903]

>>15070899
What a surprise, the abrasively ignorant rageaholic who can't comprehend imaginary numbers well enough to explain them is obsessed with putting things in his ass.

[Anonymous No.15070904]

>>15070899
kek

[Anonymous No.15070905]

>>15070902
>I still can't reasonably explain how an imaginary number is a number, so I will project my anger about my own ignorance onto others.

[Anonymous No.15070908]

If you really want to say something meaningful about whether complex numbers are or are not numbers, shouldn't you start with some useful definition of numbers generally?

[Anonymous No.15070910]

>>15070905
So I dug in my brainlet folder and found picrel. I think it truly illustrates the situation.

[Anonymous No.15070912]

>>15070908
I gave him a brainlet-friendly one but it didn't suit him because his definition of numbers is that you can divide apples by them in a way that makes "physical sense". To him. Subjectively. lol

[Anonymous No.15070913]

>>15070910
Yes it very much illustrates your complete inability to explain how an imaginary number is a number or how to divide something into i amounts, great job, you can go back now, you are no longer needed here.

[Anonymous No.15070915]

>>15070913
>it very much illustrates your complete inability to explain how an imaginary number is a number
I agree, but it also illustrates why.

[Anonymous No.15070918]

>>15070908
His attempt to do that failed, he lied about how i universally applies to all the usual arithmetic operations, was called out, and has devolved into a series of name calling fallacies ever since because he couldn't comprehend the physical corollary of -1 apples where he was unable to provide something similar for i, just referencing something about shoving things up his ass instead.

[Anonymous No.15070922]

>>15070915
Great job, visually demonstrating your deficits, you can go back now, you are no longer needed here unless you can provide a physical demonstration relating to i things.

[Anonymous No.15070925]

>>15070922
>the star shape is deficient because it doesn't fit my holes

[Anonymous No.15070927]

>>15070912
I think that's okay. He just needs to understand that other people mean something else when they talk about numbers.

We can all agree that it doesn't make a lot of sense to divide an apple into i slices, and he isn't hurting anything with his private definition.

He is simply talking about a different topic than the rest of us and using a confusing name for it.

[Anonymous No.15070928]

>>15070925
>an imaginary number is actually not a number, but I can't explain why that is either.

[Anonymous No.15070931]

>>15070927
>He just needs to understand that other people mean something else when they talk about numbers.
He can't. His brain is physically incapable of any level of abstraction higher than counting apples.

[Anonymous No.15070933]

>>15070927
>We can all agree that it doesn't make a lot of sense to divide an apple into i slices, and he isn't hurting anything with his private definition.
>H
Then why is 1/i equal to -i if it mathematically doesn't make sense to divide 1 by i?

[Anonymous No.15070934]

>>15070918
So what definition are you using for numbers? Even if it's just a hunch or you haven't thought it out yet, giving us a first attempt will make your objections clearer and more reasonable.

[Anonymous No.15070935]

>>15070934
A number is generally regarded as a quantity or value, this is not some private definition, it is the mainstream representation of a number.

[Anonymous No.15070937]

>>15070933
Dividing an apple into i slices doesn't make sense, but complex division is not about cutting up apples.

[Anonymous No.15070938]

>>15070931
So you admit you don't understand anything mathematical, especially imaginary numbers, you just have some vague abstract definitions that you assume relate to reality somehow?

[Anonymous No.15070939]

Math made it wrong having directions to numbers (-) or (i). Stupid shit, a man made horror.

[Anonymous No.15070940]

>>15070937
Ok then what is an example of something you can split up into i divisions (since division applies to i just like any other number) and how does that work in reality?

[Anonymous No.15070941]

>>15070935
Great! That's a reasonable definition.

So you're mostly concerned that complex numbers associate a direction with a quantity? It's arguable that negative numbers also have an associated direction. Can you explain why one seems legitimate to you while the other doesn't (while still using your definition of number)?

[Anonymous No.15070948]

>>15070941
>So you're mostly concerned that complex numbers associate a direction with a quantity?
Nope you simply haven't adequately explained how the imaginary domain is actually a 90 degree rotation of the real domain rather than some arbitrary designation for a quantity that doesn't actually exist as a real number.

[Anonymous No.15070956]

>>15070940
It's not about physically splitting anything. Complex "division" makes more sense if you understand it as multiplication by the multiplicative inverse of a number. Both multiplication and the multiplicative inverse are reasonable and intuitive. Multiplication scales and rotates (the scaling is the familiar real multiplication and the rotation is essentially addition). The multiplicative inverse is just the scaling and rotation necessary to undo a multiplication by a certain number (the familiar operations of division and subtraction).

[Anonymous No.15070957]

>>15070938
>you just have some vague abstract definitions that you assume relate to reality somehow?
We have concrete abstract definitions that relate to what numbers are, gigatard.

[Anonymous No.15070960]

>>15070956
Shut up. You don't understand math. If i is a real number, why can I physically divide apples into -1 parts but not i parts?

[Anonymous No.15070971]

>>15070948
You're free to pick some other set up and try it out. If your non-90-degree rotations work just as well then there's no problem with using your system instead.

I wouldn't try to convince you otherwise without at least a suggestive argument.

[Anonymous No.15070979]

>>15070960
i is not a real number. It really is a number, but not the kind of number used to talk about apple slicing.

[Anonymous No.15070985]

>>15070979
>i is not a real number
Ok, so if you admit it's fake, why do you keep arguing with me instead of ditching your insane math cult and joining intelligent people like me back in physical reality?

[Anonymous No.15070995]

>>15070985
Yes, I admit i is fake and also that I’m a massive faggot and you were right all along about i not making any sense. I’m really just a fraud that doesn’t understand it either, I apologise.

[Anonymous No.15071004]

>>15070985
Arguing about whether or not a particular number is "real" in the common sense of the word "real" is at best part of the philosophy of mathematics (which is not necessarily useful to anyone) and at worst nonsense (because the philosophy of numbers has almost nothing to do with common sense).

But that's distinct from whether or not complex numbers are useful, distinct from whether or not we can reason about them and distinct from whether or not they are numbers (although the answer to this last question is also probably not very consequential).

[Anonymous No.15071009]

>>15070995
This guy is also trans btw if that matters

[Anonymous No.15071019]

>>15070985
Is the word "so" real? I've tried slicing an apple with it but it's not working. Please hurry. The children are hungry.

[Anonymous No.15071022]

>>15071019
I've already defeated you in a formal debate. Begone from my thread.

[Anonymous No.15071027]

>>15070971
All I am hearing is you don't intuitively understand what it means either and just defer to arbitrary definitions that you can't actually relate to or justify in your experience.

[Anonymous No.15071028]

What kind of real world problem gets you an imaginary number as a solution ?

[Anonymous No.15071029]

OP is on a quest to make computer scientists look bad.

[Anonymous No.15071030]

>>15071022
If we had bet on it and were to cut up the formal debate winnings into i shares, and the first place gets half, second half of that, third half of that and so on, how much money are you owed for winning and how much do I get for second place?

[Anonymous No.15071032]

>>15071028
A lot of physics problem use complex numbers.
They literally represent electricity with complex numbers.

[Anonymous No.15071037]

Jesus OP they literally use quaternions (4D complex numbers) to handle some parts of computer graphics, and you major in computer science.
You should ask for a reimbursement because you didn't learn shit in school.

[Anonymous No.15071050]

>>15071030
You get $i.

[Anonymous No.15071051]

>>15070939
No you guys are just worthless, please stay out of this depth

[Anonymous No.15071056]

>>15071032
In the case of electric currents only the real part of the number matters in reality.

[Anonymous No.15071058]

>>15071050
How much is that in bitcoin, we can have a second round and let anon judge winner takes i BTC and what does second place get?

[Anonymous No.15071062]

>>15068097
idc to convince OP

[Anonymous No.15071068]

>>15071027
That's not quite right. 90 degrees makes intuitive sense to me. i is supposed to square to -1 and its fourth power is one, or 0 degrees (no rotation, no scaling) or 360 (one complete rotation, no scaling). Cutting 360 degrees into four equal parts gives 90 degrees, and cutting 360 degrees into two equal parts gives 180 degrees, which is halved again to give 90 degrees.

This is all very intuitive if you think about rotation.

I am simply not prepared to argue that there are no other ways of doing things. In fact, you can use 270 degrees as a square root of -1 and I'm pretty sure everything works out to be the same (although the rotations are different in the obvious way)

[Anonymous No.15071071]

>>15070368
As long as it’s free of contradictions, sure

[Anonymous No.15071088]

>>15070847
It does make sense in the zero ring

[Anonymous No.15071093]

Let's divide by i and see if we can make sense of it. This is the same thing as rotating 90 degrees in the opposite direction, which is a very reasonable thing to do, but it doesn't make sense as dividing things, because we're really just doing subtraction of distances along the unit circle.

Instead of thinking about cutting up the apple, imagine rotating the apple one quarter turn (multiplying by i) and then rotating it back to its original orientation (dividing by i).

[Anonymous No.15071096]

>>15070869
Not with a real number, because div is closed over R

[Anonymous No.15071124]

>>15071093
Since OP insists that numbers must be quantities and their operations must be reasonable and intuitive, what's wrong with considering complex numbers as radiuses and distances along the unit circle when doing multiplication or division, and considering them the equivalent Cartesian components when adding and subtracting? Those are all intuitive operations on quantities.

[Anonymous No.15071175]

>>15071093
>imagine rotating the apple one quarter turn (multiplying by i) and then rotating it back to its original orientation (dividing by i).
Rotating around which axis?
Anyway, this is how CS students are suppose to imagine rotating an object, https://www.khanacademy.org/computing/computer-programming/programming-games-visualizations/programming-3d-shapes/a/rotating-3d-shapes
Not multiplying or dividing by i.
I have used 3d modeling programs, so I get how to rotate around various 3D axis, but not around any imaginary axis.

[Anonymous No.15071192]

>>15071175
It doesn't matter. You can pick one. It sounds very much like you're trying to pretend to misunderstand, but because it's so obvious it's not very effective.

[Anonymous No.15071197]

>>15071093
That's because there isn't a knife to cut something into imaginary pieces.
It's an extension of the number line, used to ensure every polynomial has a solution.
Bottom line is if it works you don't ask questions.

[Anonymous No.15071202]

>>15071175
>>15071192
Please multiply yourself by i and into the imaginary realm.

[Anonymous No.15071229]

>>15071192
I can help the fact that the way you are trying to tell me to imagine something is better imagined in another way. If you have a link that can better explain it your way feel free to present it, but don't blame me on the fact that other superior representations exist that don't require nonsense like imagining a number that is not actually a number is a number that rotates around reality by 90 degrees.

[Anonymous No.15071315]

>>15066281
most of them.
i live in a small town (<10k residents) and i went to this uni in hs to take calc 2. you would not believe how fucking stupid these motherfuckers were, our final could have been integrating 1/x and these motherfuckers still would have failed

[Anonymous No.15071848]

>>15071229
>my way of imagining things is wrong and unhelpful in this context, but I insist on using it
>your suggestion to imagine a 90 degree rotation is beyond my abilities, despite the fact that it requires nothing more than actually understanding the meaning of words I claim to understand
At this point, I too have reached the limit of my willingness to engage someone who is poorly larping as severely mentally retarded. Even feigning ignorance can be a useful way to draw out hidden assumptions or unrecognized ignorance, but your retard act is just a pitiful attempt to get attention.

[Anonymous No.15071978]

>>15070273
>Wolfram alpha

[Anonymous No.15072055]

>>15071056
It's not that the imaginary part doesn't matter, it's that the real part is the part you can actually measure. But the imaginary part is crucial to understanding time-varying systems

[Anonymous No.15072197]

>>15066203
They are 2d vectors with multiplication defined as rotation times lengthing. When you define multiplication in this way, the math has some really convenient properties that end up being useful in physics.

[Anonymous No.15072653]

>>15071848
It is very helpful though, it is how 3d rotation is actually accomplished in practice unlike yours which you can't even post examples of while claiming it is so easy.

What part about I only don't understand what 90 degress around an imaginary axis means do you not understand? Obviously it is easy to visualize rotation around 3D axis because people have actually made programs like blender to demonstrate it, do you have a program I can use to demonstrate how reality is 90 degrees from the imaginary based on a square root function?

[Anonymous No.15072904]

>>15066203
The field of complex numbers is the algebraic closure of the field of real numbers. So every complex number is the root of some polynomial with real coefficients.
That's the most basic definition of complex numbers, the analytic properties and the fact that C is a 2d real vector space are secondary to this.

[Anonymous No.15072914]

>>15072904
>So every complex number is the root of some polynomial with real coefficients.
So if imaginary numbers are rooted in the real numbers and some kind of subset, why does everyone keep mentioning 90 degree rotations to explain the relationship?

[Anonymous No.15072944]

>>15072914
Geometrically, multiplication by a complex number is equivalent to applying some rigid transformation (a linear map that preserves angles) to the plane that leaves the origin fixed.
Examples:
Multiplying by 1 is the identity map.
Multiplying by -1 is an inversion through the origin, which is the same as a 180 deg rotation.
Multiplying by i is a 90 deg rotation counterclockwise. Consider how rotating 90 deg twice has the same effect as rotating 180 deg once. Equivalently, i*i = -1.
Likewise, multiplying by -i is a 90 deg rotation clockwise. Consider how rotating the plane 180 deg then rotating 90 deg counterclockwise is equivalent to rotating 90 deg clockwise. Equivalently, -1*i =-i.
Multiplying by 2i is equivalent to a 90 deg rotation counterclockwise followed by a dilation by a factor of 2. (Aka every point ends up on the same ray from the origin but with twice the distance)

See how we can compose multiplications of complex numbers and the resulting number represents the same rigid transformation as the composition of the transformations of the numbers we multiplied? Formally we can describe this kind of phenomenon using the language of group action or group homomorphism.
Is it starting to make sense?

Equivalently to everything I just wrote, the set of complex numbers a+bi, with a and b real, is isomorphic as a field to the set of matrices
[a -b]
[b a]
, with multplication and addition defined as usual for both sets. As an example, visualize the effect of multiplying a 2d vector by the matrix
[0 -1]
[1 0]
, and consider what complex number that matrix is isomorphic to.
I hope that helps lol

[Anonymous No.15072958]

>>15072944
>Multiplying by i is a 90 deg rotation counterclockwise
No, there is nothing about the square root function that applies any rotation, you are the one who said that i is a subset of real numbers rather than some perpendicular extra dimension. Why doesn't multiplying by sqrt(4) cause any rotation if the sqrt is some kind of rotation function?

[Anonymous No.15072973]

>No, there is nothing about the square root function that applies any rotation, you are the one who said that i is a subset of real numbers rather than some perpendicular extra dimension. Why doesn't multiplying by sqrt(4) cause any rotation if the sqrt is some kind of rotation function?
The absolute state of /sci/'s mental illness.

[Anonymous No.15072974]

>>15072958
You seem confused. i is not a real number, but it is a complex number, since it is a root of the polynomial x^2+1.
The way you write indicates that you are operating at a low mathematical level. Consider taking logic, calculus, and linear algebra to get more familiar with the concepts at play here.
>Why doesn't multiplying by sqrt(4) cause any rotation if the sqrt is some kind of rotation function?
I'm not sure who said that the sqrt is a 'rotation function'. The sqrt is multivalued, since two distinct (complex) numbers square to a given (complex) number.
More generally, z^(p/q) with z complex and p,q real and coprime, has q distinct values, so it is not really a function. If we want it to be a function, we must select a branch, and there are q branches to choose from. Note that if you raise a complex number to a transcendental power, the result of this expression is multivalued with infinitely many distinct values!
For convenience we usually just define sqrt(x) to be a nonnegative real, where x is a nonnegative real. This is the principal branch of sqrt(x). So multiplying by sqrt(4) does not rotate the plane because sqrt(4) = 2, and a positive real just dilates the plane.

[Anonymous No.15073020]

>>15066342
Two men (+) meet up and they talk about men (+).
>Bro, Demarcus is is such beast! I just hauled it in on draft kings.
Two women (-) meet up and they talk about men (+).
>OMG, can you believe that Blake just asked me out?
A man (+) and a women (-) meet up and they talk about women (-).
>Baby you're so beautiful, your my only.
>I know, isn't my hair so pretty.
Two trannies (i) meet up and they talk about women.
>Wow, this hentai waifu looks so hot in her thigh high stockings, this makes my girl dick hard.

[Anonymous No.15073023]

>>15072974
Yes because you are not a very good teacher.
Its ironic that you cite logic given that all the math definition you have taken time to memorize aren't logical and you can't seem to be able to consistently explain what you mean by rotation and why i is a rotation, also you don't seem to know what a function is either since its just a simple mapping from input to output which square root function certainly does.

[Anonymous No.15073095]

>>15073023
Okay. You aren't very smart. Have a good day.

[Anonymous No.15073136]

Here, watch this series of videos. They're short and it's worth following the build up through instead of skipping ahead.
https://www.youtube.com/watch?v=T647CGsuOVU&list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF
Part 7 gets to where the rotation aspect comes from. It's not just an arbitrary way of describing things, it appears by itself when you start trying to multiply complex numbers.
If it seems weird, think of this: doesn't it seem weird that there's no way to get a negative when multiplying a simple number by itself? Like, why is there a preferential direction that squaring goes, why does taking the root of a negative number just not work? It would feel more natural if that operation was reversible and symmetrical like the other arithmetic operations.