"Complex" (read: imaginary) numbers

[Anonymous No.9542268]

>yfw there is an entire branch of mathematics dedicated to "analysing" completely made-up numbers that have literally no physical representation in the real world
Friendly reminder that if you still take imaginary numbers seriously in 2018 you are a hopeless brainlet.

And before retards start coming in to debate this, please tell me how to get this this mythical realm of yours where one can possess 7 + 9i apples.

[Anonymous No.9542275]

>he's not an electrical engineer

Haha, faggot.

[Anonymous No.9542283]

Friendly reminder that mathematics isn't even slightly concerned with what things do and do not have a physical representation in the real world. If that causes you to not take it seriously, then perhaps you should try to actually understand some math before criticizing it.

[Anonymous No.9542285]

>>9542268
>EE
>fuckloads of imaginary shit that is real
>Matsc
>lots of imaginary shit that is real
>anything dealing with oscillatory systems and ODEs has fuckloads of complex analysis
Congrats on completing algebra 2 brainlet

[Anonymous No.9542289]

>>9542268
>what is reactance
legit u work with imaginary numbers semester 1 electronic engineering

damn op is dumb

[Anonymous No.9542323]

>>9542268
>no physical representation
>trigonometric functions not showing up all the time when describe oscillations
>euler not giving us connections between complex numbers and trigonometric functions
>no physical applications
It's like you've never taken diff EQ before.

[Anonymous No.9542326]

>>9542268
Can't you imagine apples? Just grab 7 real apples and then imagine 9 apples next to them and you're done.

[Anonymous No.9542328]

hahaha complex no. are useless lel
*gimbal locks*

[Anonymous No.9542352]

>>9542268
Quantum states are complex, so its literally physics

[Anonymous No.9542359]

>>9542268
https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

[Anonymous No.9542366]

>>9542268
>4 axes
wtf

[Anonymous No.9542401]

>>9542328
>what is matrix math

[Anonymous No.9542402]

>>9542352
True, but quantum states are not observable.

The observables in a quantum system are the eigenvalues of the Hermitian operators acting on the quantum state. And those are always real numbers.

[Anonymous No.9542407]

>>9542402
Just because it's not observable doesn't mean it's not useful; I'm sure you like computers and transistors working

[Anonymous No.9542428]

>>9542407
I agree, but op asked for an actual physical representation (which exist anyway as just points in a plane).

[Anonymous No.9542445]

>>9542268
>no physical representation in the real world
The amount of ontological assumptions here is off the wall. What exactly does it mean for an abstract entity to have a "physical representation in the real world" if I may ask? Let's take some arbitrary abstract object and call it OogaBooga. What would it mean for OogaBooga to be a "representation" of, say, a particular tree?

[Anonymous No.9542449]

>>9542268
Physics use it anything involving: rotation, waves, vibrations

>because rotation are related to waves by the formula:
[eqn]r \ e^{i\theta}=r \
(\cos{\theta}+i\sin{\theta})[/eqn]

>Since Electricity behave as waves:
EE uses complex numbers ALL THE TIME

In Circuits, Electromagnetic Waves, Electronic Signals
>with lots of applications in real world, since without such math no one would figure out how to make modern electronic devices as computers or smartphones

[Anonymous No.9542450]

Well "real" numbers aren't anymore physical than "imaginary" numbers.

Numbers dont exist at all. So why take issue with just one group?

[Anonymous No.9542454]

>>9542449
>Physics use it anything involving: rotation, waves, vibrations
*Physics use it in anything involving: rotation, waves, vibrations

[Anonymous No.9542457]

>>9542450
>Numbers dont exist at all.

[Anonymous No.9542460]

>>9542401
Euler rotation in matrix form is still limited by rotation order

[Anonymous No.9542495]

>>9542268
t. literal brainlet

[Anonymous No.9542526]

>>9542268
they're literally just pairs of real numbers with multiplication defined so that (0,1)*(0,1)=(-1,0) stop being retarded

[Anonymous No.9542635]

>>9542275
>faggot
Why the homophobia?

[Anonymous No.9542684]

>>9542268
You can't have -7 apples retard. Or even 2/3 apples.
>but you can have a apple debt or a fraction of an apple
Then you're talking about debts and fractions of apples, not apples.
They're meant to "count" or rather represent different things.

[Anonymous No.9542759]

>>9542684
Holy fuck.
What is even the point of this argument? There is no reason to try to redefine such a concept so narrowly when its inherent meaning is already obvious. Do you think you are realistically going to convince anyone to come around to this backwards-ass manner of thinking?

[Anonymous No.9542765]

>>9542759
>What is even the point of this argument?
The point of this argument is that everything you said after those words applies in EXACTLY the same way to OP's argument about complex numbers. It's a reductio ad absurdum.

[Anonymous No.9542776]

>>9542268
Complex numbers are just vectors in in R^2. You can have an apple lying in the position 7+9i relative to you.

[Anonymous No.9542783]

>>9542765
Oh, whoops. I thought you were being serious.

God, I swear someone here unironically claimed that same thing in a different thread. This place is so confusing.

[Anonymous No.9542808]

they're useful for rotations, op

say [math]1 + 1i[/math] represents the point (1, 1)

all you have to do to rotate it [math]n[/math] degrees is multiply it by [math]cos(n) + sin(n)i[/math]

so, for example, to rotate it 45 degrees, all you do is

[math](1 + 1i)(cos(45) + sin(45)i)[/math] = [math](1 + 1i)(\frac{\sqrt{2}}{2}
+ \frac{\sqrt{2}}{2}i)[/math]

so you new point would be [math]0 + i\sqrt{2}[/math], i.e (0, [math]\sqrt{2}[/math])

don't you think that's comfy? in the real world you might want to rotate some apples from something, complex numbers are a tool you can use.

[Anonymous No.9542874]

implying real numbers exist
also theyre useful for like cubic roots etc

[Anonymous No.9542917]

>retards ITT failing to grasp the point
Obviously you can use fake math to do shit with oscillations, rotations, electrical currents, vectors, waves, etc. That's not the point. The point is that, when I rotate my phone 90°, I'm not multiplying it by i. What you're doing is making an abstraction that happens to use imaginary numbers. You are taking my phone's coordinates, using fake math to convert it into complex numbers, multiplying that by i, then turning that back into actual real physically-representable coordinates.
What I want to know is where I can actually physically find i in the universe. Are there two shoes a distance of i meters apart somewhere? An apple with mass i kg? A rocket that fell to the ground after i seconds?
No? Then it's fake.

>>9542450
>>9542874
Numbers absolutely exist. I have 9 apples. I have 6 + 3 apples. I have 12 - 3 apples. I have 3 × 3 apples. I have 27 ÷ 3 apples. I do not have i apples.
>m-muh non-constructibles
Still can exist in a continuous context. There are two atoms π units apart. After e seconds, shit happens.

[Anonymous No.9542927]

>>9542268
>no physical representation in the real world
the fact that that was written on an AC-dependent device... fucking KEK

[Anonymous No.9542930]

>>9542917
Complex Numbers are useful for Physics, Electrical Engineering & Mechanical Engineering.


Unlike Poetry or Philosophy.

[Anonymous No.9542933]

>>9542917
>non-constructibles
show me -3 apples or π apples

you would have never extended the number line past the naturals, enjoy living with your head stuck in the ground

[Anonymous No.9542942]

>>9542268
>please tell me how to get this this mythical realm of yours where one can possess 7 + 9i apples.
Easy. You possess 7 real apples and you imagine 9 more. :)

[Anonymous No.9542944]

>>9542268 >>9542917

The Schrödinger equation
>the greatest formula of Modern Physics

[eqn]i\hbar {\frac {\partial }{\partial t}}\vert \Psi (\mathbf {r} ,t)\rangle ={\hat {H}}\vert \Psi (\mathbf {r} ,t)\rangle [/eqn]


the imaginary number [math]i[/math] appears in physics whenever waves or rotations are involved.

In this case (Schrödinger equation) the [math]i[/math] tells us that particles of matter behave also as waves (ie wave–particle duality)

A fundamental truth of universe

[Anonymous No.9542945]

>>9542268
t.brainlet never took a abstract algebra course or a complex analysis course.

[Anonymous No.9542978]

>>9542917
you have i apples. if you make a square of your apples, it'll just be a negative apple.

[Anonymous No.9542982]

Spotted the brainlet. Real maths (aka maths more complicated than just counting apples) works with structures so abstract and so disconnected from the real world so that complex numbers look like very friendly and down to earth object compared to them

[Anonymous No.9542985]

>>9542449
Stop, you're not proving anything. If something can't be easily and directly related to the quantity of apples then it's not real math. (Note that apples must me chosen, if you found a way to relate complex numbers to quantity of oranges or pears that still wouldn't make them real math)

[Anonymous No.9542990]

Actually, you should me more suspicious about existence of reals than of complex numbers. Given reals complex numbers are just pairs of reals with fancy multiplication. But reals, they require some weird infinite processes like adjoining infinitely many roots to Q, or making equivalence classes of uncountably many Cauchy sequences.
Even Wildberger accepts complex numbers (over rationals), and not reals

[Anonymous No.9542995]

>>9542990
>adjoining infinitely many roots to Q
that would be a proper subset of the algebraic numbers, which in turn are a proper subset of the reals

Dedekind cuts are where it's at

[Anonymous No.9542997]

>>9542995
>What is a splitting field

[Anonymous No.9543000]

>>9542997
>What is the most famous result from Galois theory

[Anonymous No.9543008]

>>9542268
Nice joke mate
>think complex analysis is useless
Haven't you worked with physics before idiot?

[Anonymous No.9543010]

>>9543000
I don't know, what is it?

[Anonymous No.9543021]

If you want to find 3th degree polynomial roots then you're forced to use imaginary numbers even if you polynomial or your roots don't contain an imaginary term

[Anonymous No.9543039]

>>9543010
For a sec I thought you meant radicals (nth roots). Algebraic numbers can't always be represented by these

Algebraics are still a proper subset of the reals

[Anonymous No.9543110]

>>9542268
>literally no physical representation in the real world
not true

[Anonymous No.9543140]

>>9542268
They work perfectly well in our system of mathematics and have led to discoveries applicable in the real world despite not being "real" themselves. What's the problem?

[Anonymous No.9543228]

>>9542917
They represent coordinates so of course saying things like (0, 1) apples and (0, 1) metres doesn't makes you stupid nonce.

[Anonymous No.9543653]

>The numbers are called imaginary therefore they must be made up
Literally fucking retarded

[Anonymous No.9543673]

>>9542268
>And before retards start coming in to debate this, please tell me how to get this this mythical realm of yours where one can possess 7 + 9i apples.
Please tell me how one can possess -7 apples. Please tell me how one can possess 2.15 apples. Please tell me how one can possess [math]\sqrt{2}[/math] apples. Please tell me how one can possess 10^100 apples. Please tell me how one can possess x apples where [math]x^2+1=0[/math].

[Anonymous No.9543682]

>>9542366
https://en.wikipedia.org/wiki/Quaternion
It's like complex numbers, but there are three distinct complex complex terms and multiplication doesn't commute. My friend who did game design said they used them sometimes for moving and rotating bodies in 3D.

[Anonymous No.9543686]

>>9542268
That is literally all of math. You can not quantify anything in the real world correctly with math a human could understand.

[Anonymous No.9543687]

>>9542783
yeah I remember that from last night, I think they tied it into Jews somehow too

[Anonymous No.9543708]

>>9543673
>you can't have apple debt or cut apples into fractions

[Anonymous No.9543948]

>>9542933
I can show you three apples, two of which are an arbitrary distance from each other, and the third is π times that distance from the first. I can also line a bunch of apples up on an axis:

Apple 1 ---- Apple 2 ------ Apple 3

And say that apple 1's position relative to apple 3's to apple 2's position is a negative number. All ratios and fractions can be represented with 3 positions as well.

However, you cannot represent i this way, because it is fake math.

[Anonymous No.9544133]

>>9542917
no two apples are exactly the same therefore it's impossible to have two in a non-abstract sense

[Anonymous No.9544141]

>>9542944
>A fundamental truth of universe
no such thing. All truths are transient.

[Anonymous No.9544147]

I guess since -1 apples can't exist, negative numbers are useless either.

[Anonymous No.9544180]

>>9542268
>doesn't know how to phase shift apples.
Why are you such a brainlette op?