Am I the only one who hates complex numbers? They seem like made

>>8649815
What are you hoping to get from this thread?

>>8649823
Maybe gets off on being verbally abused about having stupid mathematical opinions,

>>8649815

guess what? they are

the point is they are useful and clever

They're incredibly useful for problem solving. $/sqrt 2$ and π are also kinda made up but try to do simple calculations without using them and you're fucked.

>>8649866
>$/sqrt 2$ and π are also kinda made up
That's like saying that the diagonal of a square is made up.
Are you OK?

>>8649890
>square
Square with side of length one.

it's just as real as polynomial rings and their quotients

If its stupid but works then its not stupid. i is used to solve certain kinds of problems more elegantly than if we didn't have it.

>>8649823
Talk about what numbers are and how to think properly about math.

Apparently guys like newton, descartes etc werent fans of imaginary numbers either. Its a subject Id like to resolve because im stuck here.

>>8649890
Squares are made up as well

Don't talk to me or my phasors again

>>8649815
>seem like made up bullshit
>made up

Well, they're called imaginary for a reason

>>8649815
>They seem like made up bullshit to me.
That's because they are made up you fucking goof

>>8649815
just like any number

>>8649815
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.

>>8649815
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.

>>8649815
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.

>>8650239
Why invent imaginary numbers just for this? You could just represent rotation by 90-degree intervals as an element of integers mod 4

>>8650197
>Do you believe in real numbers?
No

>>8650344
Would you be ok with the rational complex numbers then? What about the Gaussian integers?

>>8649815
They are just as made up as literally anything else in math

>>8650357
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 .

>>8650239
No meme-ing, this is a very good explanation. Thank you.

>>8650588
good luck with [math]\sqrt 2[/math] pizzas

>>8650588
Try working with ψ and quantum mechanics

>>8650588
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.
>http://www.intmath.com/complex-numbers/8-ac-circuit-definitions.php
>http://www.intmath.com/complex-numbers/9-impedance-phase-angle.php
>http://www.intmath.com/complex-numbers/10-reactance-angular-velocity.php

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

>>8649846
kekel shekel

>>8649890
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.

>>8649866
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.

>>8649815
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.

>>8649823
(You)s

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

>>8650765
How many atoms are in one meter?

>>8650877
Kinematic analysis in mechanisms too

>>8649846
>gets off on
> off on off on off on off on off on off on off on off on
Lrn2communicate fgt pls

>>8649815
>>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.

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>>8649823
this

>>8649823

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

>>8649815
Someone post the pasta again.

>>8650919
>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.

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

>>8650588
confirmed for knowing 0 about electricity and magnetism.

>>8649823
KEKs from mildly pissed brainlets

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>>8650093
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

>>8650588
So you would be perfectly OK with them if they were called "imaginary aiuregais", yes?

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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

>>8650342
That would be just as made up, it just wouldn't hurt your autism as much

>>8651096
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.

>>8651096
Same reason we use a base 10 instead of base 8. We just picked one that seemed simple.

>>8649815
https://youtu.be/T647CGsuOVU

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

>>8649815
Infinity within integration and differentiation is made up bullshit too, why won't you get mad at that?

>>8649942
Squares are indeed made up insofar as imaginary numbers are made up.
>>8650608
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]

>>8651916
..and this
[math]Re(z+1)\geq 2[/math]

>>8651916
Shade the entire complex plane except for a circle of radius 1 around the origin

>>8651919
Shade the complex plane to the right from from Real=1

>>8650765
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.

>>8651096
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.

>>8652328
Atoms aren't points.

>>8652332
>Atoms aren't points.
Their centres are.

>>8649815
>They seem like made up bullshit to me.

Well duh, they are Imaginary

>>8652336
And how do you find that center?

>>8649815
Well, they are useful and unfortunately for u necessary.

>>8652351
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.

>>8652387
>it's a thought experiment
i.e. made up

>>8649815
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

>>8652330
>Or mark it on a number line.
it's marked in OP's pic...

>>8652387
>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.

>>8652399
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 /sci/. You fucked me up.

>>8650957

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.

>>8652399
>>8652432
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?

>>8652457

Your assertion is a contradiction in terms.

>>8649815
Stop being a fucking moron

>>8652432
>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!

>>8653138
But the distances exist in space, regardless as to whether something is aligning itself to them.

>>8649815
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.

>>8653198
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.

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>>8650093
This is epic

>>8653198
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.

>>8652336
An Atom is not the size of its core and an Atom's core is not a point.

>>8650746
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

>>8651208
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.

>>8652328
So would 5.069... Be equal to 5.0690...? And would ... Be equal to ...?

>>8649815
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.

>>8649815
shouldn't this be a 1-axis graph?

>>8649933
K, and Pythagoras hated them to, along with the number 0

>>8650093
>Al-Gebra
Pretty good, but the rest is too tryhard

>>8650093
Actually fucking cried. Sorrow is felt for the ignorant

>>8650938
If only there were a place where we could read about such things...

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>>8650093
>and I’m the top math deity in the entire US academic forces
I will attain this title some day

>>8650608
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)

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>>8650093
Excellent.

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>>8653477

Because natural numbers represent relationships between objects that present themselves easily in the world. It's hard to think about substance without thinking about the quantity of substance. Either you a whole substance, a portion of a whole substance, or no substance.

Try measuring an irrational or a transcendental number in the real world. Will you be able to discern the exact measurement of pi from any of your circles? Is it even physically physically possible, given that at some fundamental level, the building blocks of reality will probably have discrete lengths?

At least irrational numbers seem to mirror natural numbers in "realness" on the surface, so one can easily dismiss the problem as "trying too hard". But imaginary numbers are a serious bitch to think about. Try to intuitively understand a substance with a quantity that can be described by imaginary numbers. You fucking can't, unless you're talking about relationships between objects that we don't see on a day-to-day basis, like electric currents.

You can understand the fundamentals of electrodynamics all you want, and you can understand how imaginary numbers let you describe physical phenomena, but you will NEVER understand imaginary numbers as a descriptor of quantity. NEVER.

>>8656132
>Either you have*** a whole substance, a portion of a whole substance, or no substance.

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>>8656132

also I might just be saying bullshit because I'm a philosophy major, so tread carefully

>made up

Nothing is made up. Human brain is incapable of making anything up. Everything human knows, imagines, dreams, "makes up", comes from observations.

Entire mathematics is based on observational. Mathematics is entirely observational science. No concept in mathematics arise mysteriously from this magnificent "human imagination". They are all in nature.

So are complex numbers. What is so difficult in them, it's just a two-dimensional number you brainlet. You deal with 2-5 dimensional numbers in your everyday life constantly, but just because it's """"mathematics""" the concept is suddenly hard for you.

>>8649815
Mathematics is basically the study of relationships.

>>8656167
>What is X?
>X is Y
>What is Y?
>X is Y

You haven't informed anyone until you define "relationships".

Like do you mean me and my girlfriend? Mathematics studies my relationships? Can mathematics explain why my ex-gf was such god damn bitch?

I do hate them. They literally do not represent anything real, whereas /popsci/ fags claim otherwise. The only reason to use them is easy mathematics but calculations must always start and end with real mathematics.

>>8649815
They're basically just "plane numbers"; reals are "linear numbers". Everything follows from finding definitions that make them behave as you'd expect. Likewise, "volume numbers" can be constructed, and so forth.

Stop getting hung up on the word "imaginary".

>>8656202
you never deal with "real" numbers in reality either, it's always an approximation, but i don't see you bitching about that

>>8656132
Electrodynamics can be easily be done without complex quantity. It only helps the mathematics part.

>>8656206
>Likewise, "volume numbers" can be constructed

wrong, there's no field over R^n for any n>2

>>8656208
Oh no, I must approximate to nearest Plank unit!

>>8656212
>>8656206
well in fairness there's quaternions and octonions that act on four- and eight-dimensional spaces, but there's nothing nice for 3D.

>>8656206
Comlex plane isn't R^2. Complex numbers rotate. The integral rules aren't the same.

>>8656211

that makes no sense. you should either need the mathematics to understand it, or you shouldn't. otherwise, you're just handwaving the nuances, like when you learn about science before taking at least calculus

"the mathematics" part is for making sense of the concepts and solving problems, unless you consider it to be a "short-cut" (not the right phrase probably) and not a direct one-to-one relationship to reality

>>8656213

Then it's no longer the an irrational or a transcendental number. Thus you don't find them in reality. It's a natural or rational quantity that you measured.

The only numbers that exist and are measurable when it comes to empirical objects are real numbers and rational numbers. But I agree, they're "close enough" to not be that mind-boggling, especially since we have no measuring tools capable of being "precise enough" anyway.

But it's the same problem that we have with imaginary numbers, if only less extreme.

>>8656233
Of course it does. Let's say that you end up with a RCL circuit and you would want to solve the conserning differential equation which is a real equation. You would try a solution of form exp(r*t). But surprise, surprise the constant r could be imaginary! But no worries, it is companied with it's complex conjugate and ta-da you have solution: a sinusoidal function which is again is a real function.

>>8656259

>Of course it does. Let's say that you end up with a RCL circuit and you would want to solve the conserning differential equation which is a real equation. You would try a solution of form exp(r*t). But surprise, surprise the constant r could be imaginary! But no worries, it is companied with it's complex conjugate and ta-da you have solution: a sinusoidal function which is again is a real function.

that doesn't answer the question of what imaginary quantities mean, why they even appear, and what this means for understanding the subject

>>8656266
Jesus Christ, it's not about "complex numbers", it's simply about the structure they imply. Numbers aren't real man, no numbers are. You think they are because their connection seems so obvious, but they are not real.

>>8656278
>numbers aren't real

Interesting opinion from an entity whose entire existence is just sum of electromagnetic field equations and quantum mechanics.

>>8656266
They do not mean anything. They are a mathematical gimmick to help up with calculations.

>>8656280
Where do you see complex numbers in electromagnetic field equations?. And for the quantum mechanics yet again, it's a gimmick. Only the norm squared of the quantum wave represents, at most, something physical.

>>8656280
It's fields that are real, not numbers you dolt. The physical objects we are describing are NOT equal to the mathematics we describe them with. By that logic apples are numbers because we can count them.

>>8656291
>>8656293
Oh god brainlets; two of them!

*Anon activates his jet pack and escapes

>>8656291
>Only the norm squared of the quantum wave represents, at most, something physical.
Not correct, the phase is physical too, and thus you could arguably say that the complex number has meaning. But it's not about that anyway, it's about mixing up abstract objects with physical ones.

>>8656293
We must use real numbers to describe something physical.

>>8656298
Doesn't make numbers real. Numbers are an abstract concept, they only exist in your head.

>>8656301
Oh god who let these brainlets here. God damnit brainlet surveillance center slipping on their job.

>>8656266
You could also solve the RCL by a different method. The existence and uniqueness theorem says that the solution is unique if you find one. It doesn't matter how you find it. It just happens to be that the solution (sum of two sinusoids) can be described by complex numbers with Euler's famous formula so it is easy to try a solution of that, possibly complex, form.

>>8656301
We can have 5 apples but we cant have (27+3i) apples.

>>8656293

and you aren't bothered by the idea that you can develop a logic system to describe all relationships within a field, but the logic system doesn't correlate with the physical objects that it describes? how the hell does that work

>>8656317
Newsflash: sin(x), a difficult function but it is part of the physics. Mathematics to the rescue: sin(x)=(e^ix-e^-ix)/2. Now it is again easy to do the computations.

>>8656314
I can have 3 apples but I can't have -2 apples

>>8656327
No but -2 apples means that you remove 2 apples

>>8656337
Nope. Minus is just an operator. There are no negative numbers, there's just operator called minus.

>>8656323

you're not even answering my question. you're not my TF, and you don't need to lecture me on solutions. I can do the problems. that's brainlet tier understanding.

I just don't get how the system REALLY works.

>>8656307
>Out of arguments, get the memes!
Seriously though, if you really don't understand that abstract objects are strictly separate from physical objects, then you missed out a lot man.

>>8656314
So what? Who cares. I can't have -1 apples either. Or SU(2) apples. Not every mathematical object needs to be assigned to fucking apples in order to be valid.

>>8656317
We just use mathematics to describe things, but that doesn't make the things mathematics. I really don't know what's so hard to understand about that. It doesn't matter how well the mathematics describe reality. In particular, we don't have a correct theory of everything as of yet, which makes the idea even more ridiculous.

>>8656342

you're in debt two apples. that's two apples you don't have, but you need.

Cool it's this thread again!

>>8656346
What system are you talking about?
>>8656347
No but to be physically valid it must be, at least, a real number.

>>8656348
>need
>have
Two operators more.

"-2 apples" =
ABC
where
A = "minus", whatever that means
B = "2", whatever that means. Some say it is a "number", whatever that means.
C = "apple", whatever that means. Some say it is an "object", whatever that means.

"-2 apples" = "you need two apples for your debt, and you don't have them"
ABC = ABCDE
where
D = "have", whatever that means
E = "need", whatever that means


Humans don't make any sense in their infantile and pathetic primal logic.

>>8656357
>No but to be physically valid it must be, at least, a real number.
Says who?

>>8656348
You literally need to assume two hypothetical apples to make the abstraction work. You do all this and don't realize how abstract it is, simply because you are way too used to it to even think about it any longer. It's the same with complex numbers, you get used to them at some point. You realize how they are simply describing how some things work. That's all you need.

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>>8656347
>We just use mathematics to describe things, but that doesn't make the things mathematics. I really don't know what's so hard to understand about that. It doesn't matter how well the mathematics describe reality.

Because that's hand-waving logic for brainlets who don't want to ponder whether the mathematic relationships themselves are meaningful. It would be a tremendous coincidence to have a well-tuned system of mathematics to describe physical objects without the system mirroring the relationships between physical objects to some extent.

>complex numbers don't mean anything
>but so many physics calculations require their use, and they're necessary for some calculations
>the calculations are almost seamless, very few if any exceptions required despite their weird nature
>brainlets think this isn't even remotely suspicious

Everybody knows that abstract objects and physical objects are different. But do relationships between abstract objects mirror the relationships found between physical objects in an intuitive manner? Or is all mathematics a gimmick for understanding facts about reality? Can better analogical systems be devised?

>In particular, we don't have a correct theory of everything as of yet, which makes the idea even more ridiculous.

>we don't understand everything
>therefore don't try to understand everything

Great logic. Thanks man.

>>8656364

It's a social abstraction with tangible connections. Thinking about the future, like in debt, is perhaps one of the most intuitive forms of human thought that we have. -2 apples is going to describe 2 apples in a given situation. What is 5 + 2i apples going to describe? There's no analogy for that.

>>8649815
>It's another "Anon hasn't ready any philosophy of maths" episode

>>8656358

Operator A is related to operator D and E.

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>>8656364
Says me

>>8656368
>Because that's hand-waving logic for brainlets who don't want to ponder whether the mathematic relationships themselves are meaningful.
Nobody said it's not meaningful. It's just separate from physical objects doing shit, that's my whole point. I get that it's fascinating and all tho.

>It would be a tremendous coincidence to have a well-tuned system of mathematics to describe physical objects without the system mirroring the relationships between physical objects to some extent.
Well, we don't know yet. You can speculate what the most fundamental origin of the seemingly logical nature of physics is, but we don't really know.

>Everybody knows that abstract objects and physical objects are different.
Okay, then we are on one page.

>>8656375
Why do you even need an apple analogy? I don't get it. Is it because complex numbers are called numbers? Is that irritating you that much? You can call them complex objects then, completely abstract. Maybe that calms your mind.

>>8653482
>And would ... Be equal to ...?
what are you even asking

>>8656095
quaternions have applications tho, e.g. in computer graphics

>>8656400

>Nobody said it's not meaningful. It's just separate from physical objects doing shit, that's my whole point. I get that it's fascinating and all tho.

Of course it is. I acknowledged your point ages ago. Your last sentence is what we're bothered about.

What is the relationship? Are the logical structures analogous in some way? Or is the entire field of physics one damn miracle for solving problems and it doesn't represent any fact of nature accurately.

>Why do you even need an apple analogy? I don't get it. Is it because complex numbers are called numbers? Is that irritating you that much? You can call them complex objects then, completely abstract. Maybe that calms your mind.

>complex objects
>what kind of objects?
>they describe quantities, aka numbers

Congratulations, back to square one if you don't want to think about implications. Again, this is more brainlet hand-waving. If you haven't seen the problem yet, then you never will.

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>>8656413
They can be replaced with rotation matrices. Pic related, Der Führer rorated only by rotation matrices as I tried to simulate Wolfenstein 3D.

>>8656419
Describe in one full sentence what the problem here is exactly. Because I don't see it, you move in circles without making an actual point.

>>8656421
Yea but I thought if you don't use quaternions you have to worry about shit like gimbal lock. There's probably ways around that too, though.

>>8656423

In physics, you may need to use complex numbers in order to describe quantities of physical objects, which makes no sense intuitively and raises fundamental questions about the meaning of mathematics and physics.

Listen up rebel against God, God will not now...God has not ever...God will not ever have complex numbers. When you see a people that have elevated complex numbers to stand in the place of God-ordained proper real numbers, you are looking at a doomed people!

>>8656429
Please, provide examples

>>8656421
Jesus Christ, yes, they can be replaced with matrices because they are literally mathematically equivalent to matrices, i.e. isomorph. Quaternions are just a neat way of writing it. It's far easier to make a few calculations with quaternions instead of multiplying a bunch of matrices. And that's how you need to think about these things. Their postulation does not imply any direct correspondence to anything physical. It's just about the useful structure they span. It's that simple.

>>8656429
Absolutely nothing in modern physics makes intuitive sense. Beyond that, I still don't see the problem. The complex numbers are just describing a quantity with amplitude and phase. It's pretty well understood. Or do you have anything more concrete?

>>8656434

https://motls.blogspot.com/2010/08/why-complex-numbers-are-fundamental-in.html

>>8656431
>real numbers

Anything beyond the rationals is pure heresy.

>>8656445

God never said it was abomination to be a real number, he said it was an abomination to be a complex number.

>>8656444
I won't read that, but I guess that was why you posted that.

They are literally vectors that allow division. That's it you fucking sperg.

I just leave this here:
[eqn]a + ib \cong \left( \begin{matrix} a & -b \\ b & a \end{matrix} \right)[/eqn]
Complex numbers are just a nice way of calculating with screw symmetric two dimensional matrices.

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>>8656483

the matrix isn't real, take the redpill

Isomorhism is not equivelance. And yes, you are right, quantum wave is described mathematically shortly by on a amplitude and phase eg. Ae^2pi(px-Et)i/h. But that just a mathematical simplification, it leaves data out. No real wave a has complex part. You see this bullshit in acoustics books too, eg. Fundamentals of acoustics by Lawrence E. Kinsler. He nearly always starts, "hey guys let's reprent a wave like this y=Ae^i(wt-kx) and inserts it into an equation.

>>8649933
yea. they also hated negative numbers. so fuck everything they didn't use, amirite?

>>8656509
>Isomorhism is not equivelance.
It is not an exact equivalence but it is an equivalence of structures.

ex. Sets are isomorphic if there is a bijection

ex. Vector Spaces are isomorphic if there is a linear bijection

ex. Manifolds are isomorphic if there is a smooth bijection w/ smooth inverse

>>8656509
>Isomorhism is not equivelance.
Nice hairsplitting

>But that just a mathematical simplification, it leaves data out.
No, it doesn't. An amplitude and a phase describes the state fully.

>No real wave a has complex part.
It's just a neat way to deal with the algebra of wave functions. It makes things a lot easier. It's just mathematics man, it doesn't need to be real, it just needs to calculate useful shit.

>>8653254
> epic

> hasn't seen the navy seals meme before

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>>8649815
> Am I the only one who hates complex numbers?

Not at all. There are a lot of stupid people like you.

Complex numbers are just a further and useful expansion of the concept of number.

Stat with Counting - whole numbers
> But zog, who needs more than 1,2, many

Add zero
> How can "nothing" be a thing

Add fractions
> What is half a person? Nonsense

> Add negatives
How can something be less than nothing. I am calling you out for sorcery.

Note that negative numbers are just positive numbers in the opposite direction. So real numbers have two directions only.

Add irrational numbers
> How can an irrational thing be a number
> keep this secret

Add numbers in all directions. + = East, - = West, i = North, -i = South.
> I am a practical man. Why would I need these so-called imaginary numbers?

Complex numbers make sense, as described above. But it is wen you use them that things start to happen. They are like magic. All sorts of things that don't quite work in real numbers are beautiful and simple with complex numbers.

>>8656497
> head explodes

>>8656536
>It's just a neat way to deal with the algebra of wave functions.
The directional nature of the complex number provides a handy way to model the phase of the wave, as well as its amplitude.

>>8656536
>An amplitude and a phase
So if an acoustic wave goes fully complex values time to time, it is normal to you?
>neat way, mathematics
That what I'm trying to tell here. The wrongdoing is when you try to make physical interpretations of these mathematical gimmicks.

>>8656565
But anon, the real cardinal diretions are North [math] -\mathbf{e}_\theta[/math], South [math] \mathbf{e}_\theta[/math], West [math] -\mathbf{e}_\phi[/math] and East [math] \mathbf{e}_\phi[/math]

It is not bullshit, watch this.

1^0.5 = 1 or -1

1*-1=-1

1^0.5 * 1^0.5 = 1*1 or 1*-1 or -1*1 or -1*-1

therefore

(-1)^0.5 = 1^0.5 * 1^0.5 (50% of the time)

It is in a state of limbo like the quantum cat experiment.

>>8656587
If two mathematical structures are isomorphic you can't really say one and not the other is "actual". It just becomes a matter of convenient representation and use.

>>8656573
> that's what I'm trying to tell
Yes I was really trying to amplify your point.

> So if an acoustic wave goes fully complex values time to time, it is normal to you?

Sorry don't understand.

Another point that often you can solve e.g. real differential equations by solving a wider complex problem and then taking the real part. The complex problem may involve exponentials which are easier to deal with than trigs.

>>8656606
Ok, lets call North i now. When do we travel to i? Is i cold?
>>8656612
So a pressure wave [math]p=p_0e^{\bar{k} cdot \bar{r}-\omegat}[/math] proposed by Kinsler is competly normal to you and doesn't raise any questions?

>>8656619
[math]p=p_0 e^{ \bar{k} \cdot \bar{r} -\omega t }[/math]

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>>8649890
stooop

how do you LaTeX?

God hates complex numbers! And he saith unto them, Whosoever shall put away his reals, and construct another, committeth sin against them. Mark 10:11

>>8656565
>They are like magic. All sorts of things that don't quite work in real numbers are beautiful and simple with complex numbers.
I want to understand! I want to believe!

>>8652332
[math] \displaystyle
\\
\overrightarrow{a}= x_a + i \, y_a \\
\overrightarrow{b}= x_b + i \, y_b
\\
\overrightarrow{a}-\overrightarrow{b}
= \left (x_a-x_b \right ) + i \, \left (y_a-y_b \right )
\\ \\
i \left (\overrightarrow{a}-\overrightarrow{b} \right )
= \left (y_b-y_a \right ) + i \, \left (x_a-x_b \right )
\\ \\

i^2 \left (\overrightarrow{a}-\overrightarrow{b} \right )
= \left (x_b-x_a \right ) + i \, \left (y_b-y_a \right ) \\
= \overrightarrow{b}-\overrightarrow{a}
[/math]

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>>8656647

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>>8656647
>he didn't read the sticky

>>8656900
Contour integration is pure wizardry

>here's this ridiculous contour
>we're going to integrate this outrageously complicated complex valued function over the contour
>it's analytic in and on the contour so the answer is zero lol
>oh and look at all of these other real valued functions over some integral that we can - with very little effort - show have the same value as our complex valued one
>so those are zero as well lol

(it's even cooler and more magic with residues but cbf with the extra typing)

>>8650914

It was incredibly clear what he was saying.
Lrn2read faggot

>>8649815
They are just fine op.

>>8656900
Simplest example: every algebraic equation has a complex root and therefore can be factorized (but may have no real roots). So every real non-singular matrix has a full set f eigenvalues and eigenvectors.

The theory of the complex variable is beautiful beyond words.

After complex numbers turned out to be so incredible, people looked for the next thing, quaternions, octonions but they were eventually a disappointment for the most part.

>>8656619
Un-ask that question grasshopper.

>>8657257
>full set f eigenvalues and eigenvectors
i.e. in the complex domain

>>8650914
Are you fucking retarded?