redpill me on imaginary numbers, /sci/

>>8819380
They're a field extension of the reals that allows us to describe solutions to the equation x^2 + 1 = 0.

They can be used to model lots of different physical processes.

>>8819380
originated in 16th century Italy
https://youtu.be/_qvp9a1x2UM?t=2m20s

>>8819380

Imagine a number line. Now copy that line and turn it at 90' to the original line, and BOOM there's your complex numbers.

>>8819421
is this channel actually good or just a meme?

>people complain about imaginary numbers
>They don't realize the only numbers that exists are the positive integers

>>8819444
The only number that exists is 1.

[math]1 = \sqrt{1} = \sqrt{(-1)(-1)} = \sqrt{-1}\sqrt{-1} = i^2[/math]
Hmm...

>>8819487
you cant do that, only we can do that

>>8819487
Delete this NOW

>>8819487
i^2 is -1 retard

>>8819487
that's only a valid operation on real numbers

I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

>>8819541
I was introduced to the concept of imaginary numbers in EE classes and it made sense when applied to inductors and capacitors.
But yeah, alone it's the silliest thing ever math has done

>>8819487
DELET

>>8819541
>>8819550
I don't really know anything about this stuff but how can something with so many practical applications be considered silly, or shit?

>>8819570
the practical applications are all relatively recent
they got the stigma ages ago (eg from Descartes)

>>8819541

I stopped caring about math when I was introduced to the concept of negative numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

>>8819440
yeah its a fun little channel. nice little bits of maths without too much syntax

>>8819380
We know little about them other than they have horns.

>>8819380
they are really helpful

>>8819487
[math]
\sqrt{(-1)(-1)} \neq \sqrt{-1}\sqrt{-1}
[/math]

>>8819380
They may be called imaginary numbers but they're way more real than God is.

>>8819436
But that just sounds like a cartesian graph.

>>8819400
>We can't find a solution, so let's made up one

>>8819849
Because complex numbers and ordered pairs of reals (which are represented as Cartesian plane) are pretty much the same thing, we just made up fancy multiplication for them and usually write them down as a+bi instead of (a, b)

>>8819444
>numbers
>existing anywhere but in maths textbooks
Go and find me 1 or 52 anywhere in nature.

>>8819541
I stopped caring about math when I was introduced to the concept of natural numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

>>8819881
There is only 1

Everything that has to do with 1 is a part/fraction of 1

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>>8819380
[eqn]\text{Dont believe their lies!}[/eqn]
[eqn]1 = \sqrt{1} = \sqrt{(-1)(-1)}= \sqrt{-1}\sqrt{-1}=i^2=-1[/eqn]

>>8819380
They're a meme invented by memematitions.

Math faggots always talk about how at is objectively true, despite the fact some guy just decided one day that imaginary numbers were to be represented on a complex plane, and all work with the things has been done with them sense, and therefore all of complex analysis is bullshit.

Not math.

IMAGINARY NUMBERS ARE MENTAL ILLNESS

SAME AS NEGATIVE AND REAL NUMBERS

>>8819904
prove that [math]\sqrt{(-1)(-1)}=\sqrt{-1}\sqrt{-1}[/math]

>>8819933
*whips out cock*

>>8819904
> taking a square root without breaking it into separate plus and minus cases

wew lad

I suppose you get all confused about this:

a * a = 4
a = 2
a = -2
therefore: 2 = -2
OMG math is broken!!!

>>8819858
I'll bet you think negative numbers don't exist either

>>8819858
>>We can't find a solution, so let's made up one

It's more like this:

We can't find a solution, so that means that our number system has a limitation that prevents a solution from being found. Let's enhance the number system so that it can represent the solution.

Your criticism is like criticizing a carpenter for designing and building his own tools that help him get his job done.

>>8819885
>inventing numbers that can't exist

Mathematics is merely a catalog of objects and their properties.

Entries in that catalog include objects such as: real numbers, irrational numbers, transcendental numbers, imaginary numbers, complex numbers, and hyperreal numbers.

Every entry in that catalog exists. None of those entries "exist" any more or any less than any other entries.

Now, of course, some of the entries might be more useful in certain domains. For example, if I was running a retail store, I might choose to use rational numbers for all of my product's prices -- but on the other hand, if I was analyzing impedance in a RLC electric circuit with AC current, I might choose to model the problem using complex numbers.

Use the right tool for the job. But don't make the claim that certain tools don't exist, just because you don't know how to use them.

>>8819436
>Imagine a number line. Now copy that line and turn it at 90' to the original line, and BOOM there's your complex numbers.

You need to do more than that. You also need to state that the following relationship exists between 1 (represented by the point (1,0)) and i (represented by the point (0,1)):

i^4 = 1

With this equation, you're basically saying (very roughly) that "if you take the positive Y axis to the 4th power, it generates the positive X axis". This unifies the X and Y axes, which allows them to be viewed as representing a single number system.

>>8819380
Bro do you even Quaternion?

>>8819738
Pls explain

>>8819871
But can't you only do rotations with complex numbers and not things like shear?

>>8820368
You can do rotations with real numbers and shears with complex numbers. Shear and other things are linear mapping that are defined on vector space over a field, the field being reals, complex numbers or any other field. You can do things like shear even with [math]\mathbb{Z}/2\mathbb{Z}[/math] which consists only of two elements, 0 and 1.
You are right that multiplying vector in complex plane by complex number rotates it by the argument of the number, but that doesn't mean you can't do other transformations with them.

>>8820300
complex valued root, in particular square root, is not single valued function

>>8820300
1 =/= -1

>>8820405
So is using complex numbers or vectors just a matter of which one makes the smallest equations?

>>8819948
>unironically replying to bait
[eqn]\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}_{\mathbb{BRAINLET}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}[/eqn]

>>8820435
good post

>>8819849
Protip: that's exactly what it is, but with the additional structure of well-defined multiplication, i.e. (a,b)*(c,d)=(ac-bd, ad+bc). We write these numbers in the form a+bi and c+di where i^2=-1 as a kind of shorthand.

>>8820420
Complex numbers can be vectors, you shouldn't stick to your school definition of vector as an arrow on a blackboard. Real vector spaces can be treated as complex ones, and complex vector spaces can be treated as real, so you're kinda right, we sometimes use one of these fields and not the other just for convenience.

>>8819570

complex numbers are incredibly useful, they're just brainlets.
They're used all over physics (you can't really do QM without imaginary numbers unless you're autism tier) and to prove deep geometrical ideas in algebraic geometry and compass and ruler constructions. Also in computer graphics to represent rotations (quaternions). Not using them (if it's possible) would be a waste of time and autism

>>8820599
>waste of time and autism
As in, a waste of time, and a waste of autism, or be autism and a waste of time?

>>8820604

I meant the second one but the first one also works

>>8819955
>>8819380
>this
I have to use imaginaries all the time in quantum, only weird thing is normalization of wave functions with i with the whole sign change, idk

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>>8819380
>redpill me
gtfo pill-popping /pol/esmoker

>>8819380
Can someone get me a quick run down on this number?

>>8819487
Does i0.999... = i?

>>8819436
multiplying by i rotates it 90 degrees on the complex number plane,if you're at i+0 and multiply by i you get -1+0i

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>>8819616
I stopped caring about math when I was introduced to the concept of infinite sets. What a crock of shit. If your equation can only be solved by inventing concepts that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for analytic solutions that basically say "the correct answer is whatever the limit of the infinite sum is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

>>8819380

I used to be confused about what seemed like a bunch of made up BS as well.

https://acko.net/blog/how-to-fold-a-julia-fractal/

This is what you want. This guy did motion graphics of what imaginaries look like in action a little farther down the page. Click through all the animations. If you're on mobile, it's absolutely worth book marking until you're back at a desktop. (That goes 10x for EE inclined people, since this is the math that explains how basic circuits work.)

tl;dr they're basically a way to visualize a wave circling an axis in 3D. It's like going from (x, y) graphs to (x, y, z) graphs, while following a sine wave through that space.

>>8819487

A square root function isn't the proper inverse of a squaring function. That's why we add the plus or minus when going in reverse, since it isn't strictly defined.

Generally speaking, [math]\sqrt{a^2}=\pm a[/math]. Without this rule, the function is not well-defined as you have shown.

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>>8820996
Yeah I gave up on math when they started forcing me to use letters instead of strokes on a board. YOUR NOT THE BOSS OF ME REEEEEEEEE

>>8820961
>reals bow to i
>in contact with e
>control trigonometric functions with an iron but fair fist
>will describe the first paranormal theorems
>something
>something

>>8819380
they are an extension of the reals which make trigonometry obsolete, since you can find trajectories using a regular n-D graph/coordinate system

>>8820692
pretty much this

>>8821010
>Generally speaking
hell no, it's

[math]
\sqrt {x^2} \ne \pm x, \quad \sqrt {x^2} = \left | x \right |
[/math]

>>8820996
I stopped caring about math when I was introduced to the concept of numbers that are not 1 or 0. What a crock of shit. If your equation can only be solved by inventing concepts that can't exist, like some kind of math deity, then you are fucking wrong and the math is flawed. Same for solutions that basically say the correct answer is not either only true or only false. Thats what the math said transcribed to words but god forbid if i wrote it down in english instead of the ancient math runes the teacher would mark me wrong.

>>8821023
Yeah I gave up on math when they started forcing me to use strokes on a boards instead of the fingers of my hand. YOUR NOT THE BOSS OF ME REEEEEEEEE

Our approach to maths should take into account the fact that are minds are organic structures.

Reality to us then is our interpretation of an existence through an organic mind which constructs thoughts by biochemical reactions within our brains.

Of course we are going to fuck it up. Of course we are going to produce such absurdities as imaginary numbers. We are like ants trying to make sense of a city.

Consider what a number is. It is a measurement, defined by changing parameters which we create within our organic minds. One apple. One group of apples. One half of an apple. This is the nonsense we have created to date.

Modern mathematics is derived from fucking bean counting. Nothing more. Until we have established an absolute reference to reality which is independent of our organic consciousness we will forever be ants crawling over the cracks in the pavement underneath a skyscrapers, wondering why it gets dark at certain times, and thinking of yet more absurdities.

>>8819858
It's strange, but we found the answers before find the logic behind it. I know this is bait, but it's actually worth mentioning how common it is for mathematics to find the conclusion and then a proof later on.

>>8819444
>They don't real
9/10

>>8819487
-1=e^(i(2k+1)pi), where k in Z

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>>8820996
>outing yourself as a brainlet this hard