Am I the only one who hates complex numbers? They seem like made up bullshit to me

Squares are made up as well

Don't talk to me or my phasors again

>seem like made up bullshit
>made up

Well, they're called imaginary for a reason

>They seem like made up bullshit to me.
That's because they are made up you fucking goof

just like any number

What the fuck did you just fucking say about imaginary numbers, you little bitch? I’ll have you know I stopped caring about math when I was introduced to the concept of imaginary numbers, and I’ve been involved in numerous secret raids on Al-Gebra, and I have over 300 crocks of shit. I am trained in equations that can only be solved by inventing numbers that can't exist and I’m the top math deity in the entire US academic forces. You are nothing to me but fucking wrong. I will wipe you the fuck out with math the flaws of which have never been seen before on this Earth, mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting my secret network of algebra solutions across the USA and your IP is being traced right now so you better say "the correct answer is whatever the correct answer is", maggot. The math that says the pathetic little thing transcribed to words. You’re fucking dead, kid. I can be anywhere, anytime, and I can mark you wrong in over seven hundred ways, and that’s just if you write it down in english instead of ancient math runes. Not only am I extensively trained in unarmed combat, but I have access to the entire arsenal of the United States Logical Math Corps and I will use numbers that never lie to their full extent to wipe your miserable ass off the face of the continent, you little shit. If only you could have known what unholy flaws your little “clever” human construct was about to bring down upon you, maybe you would have held your fucking tongue. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn idiot. I will shit complex numbers all over you and you will drown in it. You’re fucking dead, kiddo.

Imaginary numbers are literally two real numbers stuck together. Do you believe in real numbers? They are dedekind cuts, a construct from the rationals. Why do people have trouble believe in imaginary numbers, but not real numbers? The leap of faith in the later is clearly much greater.

Multiplication by i is rotation by 90 degrees. Rotate twice, you get -1, then thrice, you get -i, and 4 times, wow back to 1.

Geometrically we can think, ok then like that should mean the square root of i is gonna be half of a 90 degree rotation. On a unit circle that'll be at [math]\frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2}[/math] so like is that really true though? Square it and see if you get i.

Why invent imaginary numbers just for this? You could just represent rotation by 90-degree intervals as an element of integers mod 4

>Do you believe in real numbers?
No

Would you be ok with the rational complex numbers then? What about the Gaussian integers?

They are just as made up as literally anything else in math

Idk man. I get real numbers, because they relate to things in reality.

For example, you can have 3 tables, 3.75 pizzas, etc. But you can't have 3+5i pizzas (or anything else). I just don't get it, imaginary numbers are not actual numbers, so why do people call them numbers.

Good luck with root -1 cunt

always wondered if you can go more complex into the '3rd' dimension as 2+i+j .

No meme-ing, this is a very good explanation. Thank you.

good luck with [math]\sqrt 2[/math] pizzas

Try working with ψ and quantum mechanics

just because something doesn't relate to reality doesn't mean they aren't numbers. [math]\sqrt 2[/math] must not be a number then, is what you're saying. And the root to the equation [math]x^2+1=0[/math] must not be a number either.

All real numbers are complex numbers, its just a special case of the imaginary part, Im(z), being 0.

This imaginary part exists in a separate axis, it is just not expressible in our 3D reality. However, we have come up with different ways to express them, e.g. Argand diagrams. From this so many different conclusions arise. That of contour integration, residues, Laurent series expansion, etc.

And if you think complex numbers are pointless because they have no applications, look again. They do.
>intmath.com/complex-numbers/8-ac-circuit-definitions.php
>intmath.com/complex-numbers/9-impedance-phase-angle.php
>intmath.com/complex-numbers/10-reactance-angular-velocity.php

Sorry kid, but complex numbers aren't a conspiracy made by evil mathfags.

kekel shekel

no, are YOU okay? find a real, non-made-up square in real life with sides of length 1m. the diagonal is not [math]\sqrt 2[/math] because we aren't working with points. the smallest significant point here are atoms. You'll get an approximation of [math]\sqrt 2[/math] but you won't get [math]\sqrt 2[/math]. squares that have a diagonal of [math]\sqrt 2[/math] exactly must be made up.

all numbers are made up. you can't find any of them in real life, but that doesn't mean they dont exist. our ways of writing numbers, i.e. 1, 2, 3, 4, ..., are just the language we USE to write numbers. they are not the numbers themselves. the numbers exist separately.

All of math is made up. It doesn't matter, what does matter is whether the made up structures are useful and consistent. Complex numbers are that.

(You)s

We use complex numbers to describe real phenomena in electrical engineering all the time.

How many atoms are in one meter?

Kinematic analysis in mechanisms too

>gets off on
> off on off on off on off on off on off on off on off on
Lrn2communicate fgt pls

>>made up bullshit
Like anything else in math?

Integers and real numbers are for example low-level numbers, you can relate things to them easily just by looking around.
If you want to relate complex numbers with imaginary part you simply need to go deeper into reality sort to say to relate stuff to them, because they are high-level numbers.

Genius behind invention (or discovery) behind imaginary unit is so amazing and yet so obvious and simple. It works and our universe and electronics obey them.

this

It would be interesting to know their history and how they came to be

The number system is 2D whether you like it or not. If you don't get it, GLHF

Someone post the pasta again.

>It works and our universe and electronics obey them.
That's a shit way of saying it. It's more like our universe just does whatever the fuck it does, but many things in that universe can be abstracted in a way to correspond to the structure of complex numbers.

All numbers are made up bullshit, especially the natural ones.

confirmed for knowing 0 about electricity and magnetism.

KEKs from mildly pissed brainlets

Made my day

real numbers are made up too
if imaginary numbers can be used to describe something (and they can), they're exactly as real as real numbers are

So you would be perfectly OK with them if they were called "imaginary aiuregais", yes?

plebeian question: why is i equal to the square root of minus one? Why not the square root of minus 15 or any other negative number?

i don't "hate" them. they're a little bizarre if you think about it though

That would be just as made up, it just wouldn't hurt your autism as much

Because we decided that would be the most useful unit for imaginary numbers. With [math]\sqrt{-1}=i[/math] then you can say [math]\sqrt{-15}=i\sqrt{15}[/math], which is pretty easy to deal with.

Same reason we use a base 10 instead of base 8. We just picked one that seemed simple.

youtu.be/T647CGsuOVU

A series that explains and shows "imaginary" numbers quite well.

Infinity within integration and differentiation is made up bullshit too, why won't you get mad at that?

Squares are indeed made up insofar as imaginary numbers are made up.
I think these are quaternions.

Sorry I don't have precise wording for this question, but does anyone know what I would call the set of things that imaginary numbers and quaternions are a part of?
I think it might be a Cayley–Dickson construction, or maybe a set of hypercomplex numbers?

How do I plot this in Matlab?
[math]\left | z \right | \geq 1[/math]

..and this
[math]Re(z+1)\geq 2[/math]

Shade the entire complex plane except for a circle of radius 1 around the origin

Shade the complex plane to the right from from Real=1

But if atoms are arranged in a cubic lattice, then the orthogonal distance between them is a certain value, the diagonal distance is 1.414... times that.

i is arbitrary though right? Like I could say "2+5potato" or whatever.

If i is a number them give me a decimal approximation. Like, you can say "pi" or 3.14159... etc etc. It goes on forever but you can get it to sufficient practical precision.

Someone show me the first 3 digits of i. Or mark it on a number line.

Well it is not the "square root of -1", it is a number that satisfies i^2 = -1. There are multiple square roots of -1.

Atoms aren't points.

>Atoms aren't points.
Their centres are.

>They seem like made up bullshit to me.

Well duh, they are Imaginary

And how do you find that center?

Well, they are useful and unfortunately for u necessary.

I don't know but it exists. If atoms are spaced N distance apart orthogonally, then diagonally it's 1.414N.

It doesn't even matter what objects you consider, it's a thought experiment.

>it's a thought experiment
i.e. made up

complex plane is just R2 with some added structure (i.e. multiplication by i results in a 90 degree rotation), it's just as made up (or just as real) as some cartesian grid

>Or mark it on a number line.
it's marked in OP's pic...

>It doesn't even matter what objects you consider, it's a thought experiment.
Dude, you want to argue that mathematical objects exist in the real world (they absolutely and undoubtedly do NOT), and your argument is based on a fucking thought experiment?

The thing is, yes, if you mathematically arrange the atoms in a certain way and mathematically define a center for those atoms, then you may get a square root of 2 at some point out of this. But the point really is that none of that is remotely physically possible. In particular because we can't even analytically calculate the exact state of the atoms at any given point. Your example is bullshit.

But the number exists and the points exist in space. The ratio between them is the square root of two.

It's a "thought experiment" in that you actually use your fucking head and consider such an arrangement (that undoubtedly DOES exist in many crystalline structures).

I came in here to see if I could get a better intuition around complex numbers, but now I'm skeptical of every number that isn't a natural number. Thanks Veeky Forums. You fucked me up.

This is what I think. Complex numbers mirror the logical structure of physical phenomena, so they're useful. But they don't describe meaningful quantities.

To put it another way: though the size of an object may be quantised (i.e. measured in terms of integer numbers of atoms), such quantities as position and distance between them are continuous, so any real number is valid potentially.

So if atoms are arranged on a square lattice, then the diagonal distance is 1.414 that of the orthogonal one.

Is it an arbitrary definition like how any number raised to the power of zero is 1, just to make the maths work?

Your assertion is a contradiction in terms.

Stop being a fucking moron

>that undoubtedly DOES exist in many crystalline structure
They do not you fucking idiot. The world is not a undergrad exercise. You will never find a lattice in the real world that is mathematically perfect.

And again, your fallacy is that your whole arrangement requires mathematics to be setup. It's not real.

WOT U SAYIN' 'BOUT MY IMAGINARY NUMBERS PLEB!

But the distances exist in space, regardless as to whether something is aligning itself to them.

Sure, they are made up, but they are necessary for comprehensiveness in Mathematics.
Let's take, for example, the natural numbers as the starting point. Using the 4 basic arithmetic operations, you could end up in the same set, or end up with an undefined set of numbers, in this case, the only possible undefined ones are the integers, and rationals, so you should define those as well, to have consistency in your work.
If you expand the number of operations that can be applied to the elements of the sets you already defined, then you might be able to create new sets from those, when you add in exponentiation, for example, as an operator, you get the real set and the imaginary set, that are necessary for completeness' sake.

No, distances in the sense of a metric are a mathematical concept. Especially when you define the positions of whatever you want to measure the distance of. It makes no sense man.

This is epic

Distances in units of what?

Unless you define your unit based off some physical thing then it's just total abstraction like maths. Even if you get a physical unit it's impossible to know that unit with infinite precision.

An Atom is not the size of its core and an Atom's core is not a point.

Unless stupidity equals evil or should I put that in numbers? ()-1()=()(-12)()

Why are natural numbers any more acceptable than complex? In both cases, they only represent RELATIONSHIPS between other things, not things in and of themselves /thread

Wouldn't base 8 be base 10 because 8 in base 8 would be 10? I think I just proved bases don't exist. It's free knowledge woke bomb and youre feeling the energy wave flow through you.

So would 5.069... Be equal to 5.0690...? And would ... Be equal to ...?

I know of numbers that are like at least a shit ton higher (pun) than i on the imaginary axis. None of the can be expressed in text.

shouldn't this be a 1-axis graph?

K, and Pythagoras hated them to, along with the number 0

>Al-Gebra
Pretty good, but the rest is too tryhard

Actually fucking cried. Sorrow is felt for the ignorant

If only there were a place where we could read about such things...

>and I’m the top math deity in the entire US academic forces
I will attain this title some day

theoretically yes but you really wouldn't need to because the complex plane is closed to all operations(you cant get a number that doesn't belong to it no matter what you do)

Excellent.