/sci/ - Science & Math

[Anonymous No.9280788]

How can we use imaginary numbers when you can't take the square root of -1

[Anonymous No.9280795]

The whole idea of imaginary numbers is that you come up with an arbitrary number i that is the square root of -1. i is not a real number, it's just the square root of -1. Most of the "uses" or applications of imaginary or complex numbers involve finding situations where i is squared, and you end up with -1 again. Fundamentally though "you can't take the square root of -1" is only true for real numbers; with complex numbers you can take the square root of -1, and its value is i.

[Anonymous No.9280800]

>>9280795
>The whole idea of imaginary numbers is that you come up with an arbitrary number i that is the square root of -1.

No it's not. i^2 = -1 but sqrt(-1) is undefined.

[Anonymous No.9280802]

imaginary numbers is proof that contemporary people don't care about their educations. They're worthless garbage that just dumb the lesson down, and in the process, the person's understanding of the lesson.

[Anonymous No.9280805]

>>9280802
They help with understanding dimensions and things like fibration

[Anonymous No.9280838]

>>9280800
Well, you're right that I was wrong about it, but sqrt(-1) is either i or -i for complex numbers, not undefined.

[Anonymous No.9281008]

>>9280802
I believe that the real numbers themselves are far more controversial then constructing the imaginary numbers from the rationals.

In later case you just define a few things in the other you need a shit ton of construction.

[Anonymous No.9281147]

>>9280800
ja visst

[Anonymous No.9281178]

>mathematicians tell your stupid young ass that you can't take the square root of -1
>then, hoping you've become smarter and more open minded tell you there is actually a way to do that
>b-but you can't do that, it is known, complex numbers are imaginary, we can't use them

[Anonymous No.9281202]

>>9280788
You can't. The idea of "complex numbers" is entirely arbitrary and non rigorous by definition.

[Anonymous No.9281296]

>>9280838
Wrong. The square root by definition is always positive. That is sqrt (x^2) =|x|
sqrt(-1) is defined as i. I don't see the problem.

[Anonymous No.9281385]

If we can just say that root -1 is i why can't we do the same with something like ln(-1)?

[Anonymous No.9281386]

>>9280788
It's all about breaking the 3rd dimension.
We are currently limited to the 2d plane of numbers when squaring or rooting.
Using i opens up another dimension.

[Anonymous No.9281536]

>>9281385
You can, but there's no need for it.
i was defined in order to ensure that every nth degree polynomial has n roots.

[Anonymous No.9281570]

>>9281296
|i| =/= i

[Anonymous No.9281882]

If you're really uncomfortable with the idea of i, just work with ordered pairs of real numbers. Define "addition" as (a,b)+(c,d) = (a+c, b+d) and "multiplication" as (ac - bd, ad + bc).

[Anonymous No.9281891]

>>9281385
That would be i*pi*(2k + 1/2) for any integer k.

[Anonymous No.9281902]

>>9280788
i is x+<x^2+1> in the extension field R[x]/<x^2+1> of R.

[Anonymous No.9281904]

1x10^-2
sqr root = ^.5 = -1^.5

[Anonymous No.9281914]

>>9281385
You can, but you usually leave the left side of the real axis when you define ln, so that it can be continuous (and differentiable).
Instead of that you can define a new ln on the whole plane minus any simple curve starting from the origin and ending at infinity.

[Anonymous No.9282596]

Anything you want to represent using complex numbers can be equivalently represented in simpler terms which do not rely on imaginary numbers or the complex number plane.

[Anonymous No.9283102]

>>9282596
but then it won't do the cool Euler's formula thing in the complex plane, that's important to me

[Anonymous No.9283117]

>>9282596
complex differentiation cannot be expressed in simpler terms with other methods
if you use multivariable differentiation to emulate complex differentiation, then you have to have to shoe horn the Cauchy-Riemann equations separately

[Anonymous No.9283168]

>>9283117
or you can just look whether [math]d f \in \mathbb{R} \times SO(2)[/math]

[Anonymous No.9283231]

>>9280795
>>9280800
>>9280838
>>9281296
>>9281570
Help me, these faggots confused me and i'm brainlet. Can anyone clarify their points?

[Anonymous No.9283251]

>>9280802
>abstract concepts are for fags

[Anonymous No.9283275]

>>9281296
what does it mean for a complex number to be "positive" ?

[Anonymous No.9283325]

>>9280788
Imaginary numbers are one of the worst naming decisions in the field. Call the complex numbers like those of us who actually need to consider them for real world applications.

[Anonymous No.9283370]

>>9283275
What I mean is that sqrt(-1) is always i. That's by definition.
You're thinking of
x^2 = -1
Which has solutions i and -i

[Anonymous No.9283374]

>>9283275
The coefficient being positive in this case. So |b|i

[Anonymous No.9283405]

>>9281008
the 'defnintions' are a shortcut that fail to help the person in the long run. They can't extrapolate any of the lessons because they demanded to be taught the most short-sighted formulatoin possible, one that does not allow them to actually understand the lesson, just find the answers.
>>9280805
they do, but the person should just learn the hard way so they can better use their skill
>>9283251
>huuuuuuuuuuuuuuu

[Anonymous No.9283505]

>>9283405
>They can't extrapolate any of the lessons because they demanded to be taught the most short-sighted formulatoin possible, one that does not allow them to actually understand the lesson, just find the answers.
I don't think anyone can really appreciate complex numbers and how they work until they deal with electromagnetics. Although stuff like taylor series and how a calculator computes trig stuff should give enough appreciation on their own.

[Anonymous No.9283537]

Because the square root of negative one exists, imaginary and complex numbers must exist.

[Anonymous No.9283542]

>>9281882

pretty much how i think about it. call me a brainlet, but imaginary numbers are strange imo

[Anonymous No.9283670]

>>9280788
>you can't take the square root of -1

I really wish we could just permaban anyone who starts a thread with a frog picture. It's always a shitpost.

[Anonymous No.9283685]

>>9281178
literally this.

[Anonymous No.9283689]

>>9283102
This. Euler's Identity is the most beautiful thing that exists anywhere forever.

[Anonymous No.9283693]

>>9280788
Imaginary numbers can be used to find every possible Pythagorean triple

[Anonymous No.9283746]

>>9283689

indeed, many tattooed math majors have informed me of this.

[Anonymous No.9283752]

Remember when teachers in elementary school told you you can't subtract bigger number from a smaller, and later you were introduced to negative numbers? Same with complex numbers, first teachers tell you you can't take a square root of a negative number, but later you're introduced to complex numbers

[Anonymous No.9283754]

>>9280800
Not true, if √-1 weren't defined then i wouldn't be either

[Anonymous No.9283756]

>>9283374
Is 1-i positive?

[Anonymous No.9283764]

>>9281202
retard

[Anonymous No.9283778]

>>9281202
Same goes for so called real numbers

[Anonymous No.9283781]

>>9283752
You still can't subtract a bigger number from a smaller one, unless you create an arbitrary context of reference that allows it. In fact you always have a subtraction limit, you write about subtracting a bigger number from a smaller but you are not doing it, you are either subtracting a smaller from a bigger new pair of numbers or subtracting and adding what is left. No relation with the root of -1 except the fact that a teacher told you couldn't and another told you could do it. Ridiculous.

[Anonymous No.9284866]

>>9283781
Are you retarded?

[Anonymous No.9284871]

negative numbers aren't real like how can you have negative 2 apples lmao, negative apples don't exist and neither do negative numbers

[Anonymous No.9284978]

>>9280788

Yes
Square root my ass = -1
Because my ass is so amazing.