/sci/ - Science & Math » Thread #12564901

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why tf

Anonymous Sun 10 Jan 12:27:35 2021 No.12564901 View Reply Original Report

Quoted By: >>12564969 >>12565624 >>12566118 >>12566232 >>12566486 >>12566919 >>12567016 >>12567539 >>12567795 >>12567807 >>12568380 >>12568419 >>12568746

Seriously, what’s the actual purpose of imaginary numbers? Do they have any real use/applications?

Anonymous

Anonymous Sun 10 Jan 2021 12:30:34 No.12564908 Report

Quoted By: >>12564922

Seriously, what’s the actual purpose of posting this thread all the time? Is shiposting really that enjoyable or is your life just that pathetic?

Anonymous

Anonymous Sun 10 Jan 2021 12:31:52 No.12564915 Report

Quoted By:

imagine being a realcel
t. chadinary

Anonymous

Anonymous Sun 10 Jan 2021 12:34:11 No.12564922 Report

Quoted By: >>12564936 >>12564941 >>12564944 >>12565099 >>12566404 >>12566486 >>12566908 >>12567625 >>12567786 >>12568761

>>12564908
serious question, why can't they just say that the number cannot compute like when you divide by zero? They don't make up some imaginary value for a number divided by zero, but they do for finding the root of a negative number (which doesnt exist)?

Anonymous

Anonymous Sun 10 Jan 2021 12:40:12 No.12564936 Report

Quoted By:

>>12564922
this

Anonymous

Anonymous Sun 10 Jan 2021 12:43:27 No.12564941 Report

Quoted By:

>>12564922
> but they do for finding the root of a negative number (which doesnt exist)
serious answer, they do exist just as much as the roots of positive numbers. both are defined by some axioms that produce an answer and both can be manipulated in a rigorous and self-consistent manner by those rules.

Anonymous

Anonymous Sun 10 Jan 2021 12:43:40 No.12564944 Report

Quoted By:

>>12564922
I'm not a mathfag but I imagine the difference is that dividing something by zero is literally absurd notation, whereas in a negative square root the notation makes sense but a real solution does not exist.

In the first case you are going against the very rules of the notation and language. You can't divide something into zero parts.

Anonymous

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Anonymous Sun 10 Jan 2021 12:46:11 No.12564951 Report

Quoted By:

Anonymous

Anonymous Sun 10 Jan 2021 12:52:59 No.12564969 Report

Quoted By: >>12565099

>>12564901
Yeah, they rotate stuff

Anonymous

Anonymous Sun 10 Jan 2021 13:56:59 No.12565099 Report

Quoted By: >>12567484

>>12564969
This is the most intuitive way to understand them. If you want to switch a number's "direction" to an opposite one, i.e. rotate it by 180 degrees, you multiply it by -1. But what if you wanted to rotate it less than 180 degrees? Or if we rotated it by 180 degrees but in two equal steps, what would that look like mathematically? For a number a, it would be like a*x*x, where x*x=x^2 must equal -1. x would have to be the squareroot of -1, in other words i. So a*i would be a, except it's direction in a 90 degrees angle with a.

>>12564922
Because division by zero results in contradictions. Even if you said that the definition of an imaginary number is a contradiction itself, you couldn't prove that it results in other contradictions. If we assume division by zero is a legit operation, we can prove that 1=2. Or any number equals any number, for that matter. Math completely falls apart. The same doesn't happen with imaginary numbers.
https://en.wikipedia.org/wiki/Mathematical_fallacy#Division_by_zero

Anonymous

Anonymous Sun 10 Jan 2021 18:06:51 No.12565612 Report

Quoted By:

They help math if it involves sine or cosine. Some faggots just dont understand that the starting and ending should be real always. If you have some fancy and gay graph in compl*x plane, keep it within yourself.

Anonymous

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Anonymous Sun 10 Jan 2021 18:12:19 No.12565624 Report

Quoted By: >>12566106

>>12564901
Yes they are real. The imaginary thing is just a misnomer.

Anonymous

Anonymous Sun 10 Jan 2021 18:19:55 No.12565646 Report

Quoted By:

Ahlfors or Gamelin?

Anonymous

Anonymous Sun 10 Jan 2021 21:12:12 No.12566106 Report

Quoted By:

>>12565624
No. The name is justified. As cross products are pseudovectors, these are imaginary numbers. AND THEY HAVE A CONNECTION 7 dimensional cross product is direct consequence of octanions. As cross product is related to quaternions.

Anonymous

Anonymous Sun 10 Jan 2021 21:14:20 No.12566118 Report

Quoted By:

>>12564901
If it actually exists why did they call it imaginary?

Mathtards btfo eternally

Anonymous

Anonymous Sun 10 Jan 2021 21:26:16 No.12566151 Report

Quoted By:

Cyclic phemonema which are sine functions can be modeled as exponential funcrions that have an i in the exponential beacuse the laws of differentiaion say they r equal

Anonymous

Anonymous Sun 10 Jan 2021 21:52:35 No.12566232 Report

Quoted By: >>12566295

>>12564901
They are crutches. They don't exist, someone arbitrarily came up with the idea to force an answer.

>do they have any real use/applications
They are used when the model is appropriate for it. They do not represent anything. They're used in electronics or some shit where there's stuff that goes on and off.

Anonymous

Anonymous Sun 10 Jan 2021 22:18:30 No.12566295 Report

Quoted By: >>12566461 >>12567178

>>12566232
They do exist the 'imaginary' name is a misnomer as someone said. For polynomials with high degrees which I'm sure many have seen where some roots can't be computed. It is theorized the highest power say 5 will have 5 roots but in the real plane this is not always the case. The imaginary number fills in the missing roots and it actually means something. It is used a lot in ordinary different modeling oscillating systems and as you mentioned electrical systems. The application of i all depends on the system it is being applied to. It solves a lot of problems that mathematics had and is used often just like constants of pi and e.

Anonymous

Anonymous Sun 10 Jan 2021 22:58:50 No.12566404 Report

Quoted By: >>12566444 >>12566676

>>12564922
Because it is useful and arises naturally from physics, like alternate currents for example. Division by zero doesn't.

By the way, this question just came into my mind, any physifag around? Mathematically speaking, what is the black hole singularity? Is it some disguised division by zero, so that's why it fucks up the model?

Anonymous

Anonymous Sun 10 Jan 2021 23:06:31 No.12566444 Report

Quoted By: >>12566480

>>12566404
Alternative currents can be described with sinusoids. Black hole is just a gay place where even photons are kept as gimps by gravity.

Why you are making science some fuckwit religious ideology where everything should be some kind of mystery.

Anonymous

Anonymous Sun 10 Jan 2021 23:10:04 No.12566461 Report

Quoted By: >>12566477

>>12566295
If its not zero. Its then not zero. Stop forcing them. The real fundamental theory of algebra says first and second degree polynomials.

find roots to this polynomial, fag: g(x)=3

Anonymous

Anonymous Sun 10 Jan 2021 23:14:47 No.12566477 Report

Quoted By: >>12566497

>>12566461
Then you need to tell calculus and limits to stop existing and forcing what ifs when dividing by zero.

Anonymous

Anonymous Sun 10 Jan 2021 23:14:53 No.12566480 Report

Quoted By: >>12566497

>>12566444
Sum two sinusoids out of phase and with different amplitudes without using complex numbers.

Anonymous

Anonymous Sun 10 Jan 2021 23:16:20 No.12566486 Report

Quoted By: >>12566505

>>12564901
Complex multiplication is 2D rotation and scaling. It makes a lot of things in trigonometry easier.

>>12564922
It depends on the problem. For most problems you encounter at the high school level, saying there are no solutions makes sense. One of the big places complex roots become important is in linear algebra. Read up on characteristic polynomials, eigenvectors, and eigenvalues if you want to learn more.

Anonymous

Anonymous Sun 10 Jan 2021 23:19:39 No.12566497 Report

Quoted By: >>12566507 >>12566584

>>12566480
I will if you tell me how you do it with complexes
>>12566477
I will try someday. The princliple should be the algorithm. Not to force it as a number. Only successors are. And none.

Anonymous

Anonymous Sun 10 Jan 2021 23:22:34 No.12566505 Report

Quoted By:

>>12566486
Eigenvector should be in same direction when multiplied by matrix itself. If you force them matrices too, the result is 2x1x2x2 cell...and that is only for 2x2 matrices.

Anonymous

Anonymous Sun 10 Jan 2021 23:22:57 No.12566507 Report

Quoted By: >>12566532

>>12566497
Yeah you don't get to decide how math works. Got decades of it doing its job and solving problems.

Anonymous

Anonymous Sun 10 Jan 2021 23:32:06 No.12566532 Report

Quoted By: >>12566538 >>12566801

>>12566507
The negative impact is huge. Quantum mechanics have no credibility. Some complex wave function is ASSUMED i.e. Schrödinger's. If you lose real numbers you lose reality. And therefore you are in an imagination land. Quick imagination trip in the middle of calculation do possibly not harm but if starting or ending is that, then its just not valid

Anonymous

Anonymous Sun 10 Jan 2021 23:34:36 No.12566538 Report

Quoted By: >>12566589

>>12566532
what makes studying complex numbers different from studying other algebraic structures such as the ring of 3x3 matrices, or the group of permutations on 6 elements?

Anonymous

Anonymous Sun 10 Jan 2021 23:51:27 No.12566584 Report

Quoted By: >>12566594

>>12566497
>I will if you tell me how you do it with complexes
Just sum.

Anonymous

Anonymous Sun 10 Jan 2021 23:51:51 No.12566589 Report

Quoted By: >>12566626

>>12566538
Arent these all just useless math garbage? These have no concept of reality. They do not represent reality as it is.

It should be limited what should be published. If something cannot be represent with list of real numbers and with well defined operators, it probably is just someone trying to fool scientifical community for big $$$

Anonymous

Anonymous Sun 10 Jan 2021 23:55:33 No.12566594 Report

Quoted By: >>12566660

>>12566584
Sorry for being this basic, but it is just that. A simple vectorial sum, if you're using the rectangular notation. For polar coords, do this https://www.youtube.com/watch?v=6R2_afa86nA

Anonymous

Anonymous Mon 11 Jan 2021 00:05:29 No.12566626 Report

Quoted By: >>12566660

>>12566589
you saying that the ring of 3x3 matrices or the group of permutations on 6 elements (or complex numbers for that matter) cannot be represented with "lists of real numbers and well defined operators"?

Anonymous

Anonymous Mon 11 Jan 2021 00:18:25 No.12566660 Report

Quoted By: >>12566743 >>12566899

>>12566626
They have no meaning.
>>12566594
I can add two sines sin a + sin b. There.

And also if they are angle c off, use sum formula.

Anonymous

Anonymous Mon 11 Jan 2021 00:25:30 No.12566676 Report

Quoted By:

>>12566404
A black hole is basically a converse photon. Photons trade mass for energy, black holes energy for mass.

Anonymous

Anonymous Mon 11 Jan 2021 00:42:08 No.12566743 Report

Quoted By:

>>12566660
do 1x1 matrices have a meaning?

Anonymous

Anonymous Mon 11 Jan 2021 01:03:48 No.12566801 Report

Quoted By:

>>12566532
what's your level of education? i hope you realize how retarded you sound

Anonymous

Anonymous Mon 11 Jan 2021 01:54:09 No.12566899 Report

Quoted By: >>12568366

>>12566660
>summing sinusoids is just summing sin(a) +sin(b)

Retard alert! Retard alert! Someone here doesn't have the most remote clue about what a sinusoid is! Maybe you should go to a board full of retards like you, like >>>/v/

Anonymous

Anonymous Mon 11 Jan 2021 01:57:46 No.12566908 Report

Quoted By:

>>12564922
people tried this in the past, for example Brahmagupta in the 1st millenium.
however, it obviously leads to absurdities, so it was quickly discarded as an idea

Anonymous

Anonymous Mon 11 Jan 2021 02:04:41 No.12566919 Report

Quoted By:

>>12564901
AC circuits

Anonymous

Anonymous Mon 11 Jan 2021 02:53:25 No.12567016 Report

Quoted By:

>>12564901
The mirror dimension

Anonymous

Anonymous Mon 11 Jan 2021 03:46:09 No.12567178 Report

Quoted By:

>>12566295
Show me an imaginary number. In fact, show me a number. Where is it?

Anonymous

Anonymous Mon 11 Jan 2021 06:25:03 No.12567484 Report

Quoted By: >>12567556 >>12567727 >>12568067

>>12565099
>But what if you wanted to rotate it less than 180 degrees?
So it's basically adding a 2nd dimension to the number. Why not just use some convenient notation to tell which dimension is which instead of involving the nonsense the square root of -1 is? And then there are quaternions that are just further fagging this gay shit up.

Anonymous

Anonymous Mon 11 Jan 2021 06:59:23 No.12567539 Report

Quoted By:

>>12564901
>Do they have any real use/applications?
A lot in electrical engineering

Anonymous

Anonymous Mon 11 Jan 2021 07:13:14 No.12567556 Report

Quoted By: >>12568017

>>12567484
The matrix notation of complex numbers does exactly what you describe.

Anonymous

Anonymous Mon 11 Jan 2021 07:58:51 No.12567625 Report

Quoted By: >>12567762

>>12564922
>They don't make up some imaginary value for a number divided by zero
HOLY FUCK!
You are onto something here. Its about time there was an imaginary value for a number divided by zero.
Let x be any number, even gay ass faggot imaginary numbers, which as we all know are writhing with all sorts of disgusting diseases.
Take x/0
Let's define the answer as f ( f as in faggot )

So x/0 = f

PROBLEM SOLVED!

BY DEFINITION! Ho! No one can prove me wrong because its by FUCKING DEFINITION!
Now we are doing math just like the "professional" faggots who make up shit simply by invoking MOTHER FUCKING DEFINITIONS which they pulled out their shit encrusted arseholes that constantly leak pus because they like anal sex so much! Then they strut around thinking they are superior but really they are totally fucking retarded!

Whoah! Fuck! Gimme a NOBLE fucking PRIZE!

Anonymous

Anonymous Mon 11 Jan 2021 08:50:54 No.12567727 Report

Quoted By: >>12568017

>>12567484
>Why not just use some convenient notation to tell which dimension is which instead of involving the nonsense the square root of -1 is?
that's exactly what complex numbers are, a convenient notation to treat certain class of 2D transformations.

Anonymous

Anonymous Mon 11 Jan 2021 09:03:18 No.12567762 Report

Quoted By:

>>12567625
someone did calculus using the hyperreals the other day, wish I could remember how it worked
i.e.
0 -> ?
? -> ?
this way, "orders of zero", "orders of infinity" could be well defined

Anonymous

Anonymous Mon 11 Jan 2021 09:12:33 No.12567786 Report

Quoted By:

>>12564922
there absolutely exist structures where division by zero is possible. for example the projectively extended real line $\mathbb{R} \cup \{ \infty \}$ . here $\frac{x}{0} = \infty$ with the exception of $\frac{0}{0}$ which is still undefined.
the thing is that complex numbers have similar algebraic properties as real numbers (namely it's a field), which makes them very flexible (and interesting to study). division by zero contradicts laws of arithmetics. that doesn't mean it's "forbidden" to define it however you want, it means that no matter how you do it, the resulting structure will not be very nice.

Anonymous

Anonymous Mon 11 Jan 2021 09:16:20 No.12567795 Report

Quoted By:

>>12564901
Take a point on the real axis in the Cartesian plane, (x, 0). Multiply it by -1: you get (-x, 0) which is the point you obtain by a rotation of 180°. If you rotate by 90° two times in a row, you also get a rotation of 180°. So a rotation of 90° corresponds to a number that multiplied by itself has the same effect of -1. So the ordered pair (0, 1) is a square root of -1.

Also, if you don't accept imaginary numbers, you can solve cubic equations only when they have one real root; you can't solve them when they have three real roots. Which would be odd, since all the roots are real yet you wouldn't be able to reach them because you don't wanna pass through imaginary numbers.

Anonymous

Anonymous Mon 11 Jan 2021 09:20:22 No.12567807 Report

Quoted By:

>>12564901
The complex numbers are very natural.
It's the usual vectors of the plane along with a multiplication operator which is performed by multiplying the vectors' length and adding the angles.

Anonymous

Anonymous Mon 11 Jan 2021 09:32:10 No.12567844 Report

Quoted By:

OP clearly never passed anything beyond Cal 3.

Imaginary numbers are crucial to understanding and modeling any kind of differential system, such as an electrical network that can be reduced using Laplace transforms (dependent on imaginary numbers) or signal analysis via fourier transform (dependent on imaginary numbers). Or how about in pchem, modeling the nonideal gaseous interactions.

Anonymous

Anonymous Mon 11 Jan 2021 10:19:14 No.12568017 Report

Quoted By:

>>12567556
>>12567727
But where does (-1)^0.5 come from and for what reason?

Anonymous

Anonymous Mon 11 Jan 2021 10:34:40 No.12568067 Report

Quoted By: >>12568155

>>12567484
>Why not just use some convenient notation to tell which dimension is which instead of involving the nonsense the square root of -1 is?
you involve the square root of -1 nonsense because you can rotate those two dimensional numbers conveniently with it.

Anonymous

Anonymous Mon 11 Jan 2021 11:04:54 No.12568155 Report

Quoted By: >>12568159

>>12568067
Why not just stick to vector algebra?

Anonymous

Anonymous Mon 11 Jan 2021 11:06:56 No.12568159 Report

Quoted By: >>12568207

>>12568155
what do you mean? why do we use a+b*i instead of (a,b)?

Anonymous

Anonymous Mon 11 Jan 2021 11:25:06 No.12568207 Report

Quoted By: >>12568279 >>12568306

>>12568159
Yes, it's more straightforward, especially when going further into lovecraftian horrors of hypercomplex numbers

Anonymous

Anonymous Mon 11 Jan 2021 11:48:55 No.12568279 Report

Quoted By:

>>12568207
>it's
I mean vectors obviously

Anonymous

Anonymous Mon 11 Jan 2021 11:59:48 No.12568306 Report

Quoted By: >>12568590 >>12568678

>>12568207
you're just arguing against a notation, not against a concept. and the notation is convenient.

Anonymous

Anonymous Mon 11 Jan 2021 12:27:30 No.12568366 Report

Quoted By:

>>12566899
no shit, we saw that from the first post of this. entire fucking forum is full of high school faggots/baiters

Anonymous

Anonymous Mon 11 Jan 2021 12:34:18 No.12568380 Report

Quoted By:

>>12564901
very useful for oscillations and everything that comes from it (mechanical waves and vibrations, electromagnetics, quantum theory)

Anonymous

Anonymous Mon 11 Jan 2021 12:55:32 No.12568419 Report

Quoted By:

>>12564901
so that j can fuck you over in python.

Anonymous

Anonymous Mon 11 Jan 2021 14:28:23 No.12568590 Report

Quoted By: >>12568611

>>12568306
>notation
More like a way to make simple things look complicated, though it seems to be a favorite pastime of way too many mathematicians

Anonymous

Anonymous Mon 11 Jan 2021 14:36:55 No.12568611 Report

Quoted By: >>12568642

>>12568590
how the fuck is writing i = (0,1) making things more complicated, it's the exact opposite

Anonymous

Anonymous Mon 11 Jan 2021 14:41:52 No.12568630 Report

Quoted By:

As you know, multiplying two of the SAME number will never give you a negative. -2 * -2 will never be -4. Imaginary numbers let us have square roots for negative numbers. Thanks to imaginary numbers, there’s a square root of -4. So now we can solve quadratic equations and solve previously unsolvable real world problems. It’s just helpful notation. The “real” numbers on a horizontal number line with fractions, positives and negative numbers aren’t enough

Anonymous

Anonymous Mon 11 Jan 2021 14:47:56 No.12568642 Report

Quoted By: >>12568665

>>12568611
And the rest? Straightforward and easy to understand vector math with real numbers vs inventing The Thing That Should Not Be (but somehow is)

Anonymous

Anonymous Mon 11 Jan 2021 14:56:20 No.12568665 Report

Quoted By:

>>12568642
what rest? complex numbers literally are straightforward and easy to understand vector math (or matrix math). you're not saying anything else than "don't write a+bi, write (a,b)"

Anonymous

Anonymous Mon 11 Jan 2021 15:02:29 No.12568678 Report

Quoted By: >>12568795

>>12568306
The complex numbers are equipped with a natural notion of multiplication, while R^2 is not. This makes the complexes so much easier to work with in nearly every context. Sure, R^2 is useful theoretically for understanding vector spaces as a whole, but the complexes are unbeaten in their simplicity and power in extending elementary algebra/calculus. It's like, have you ever even seen the R^2 representation of the Riemann zeta function? blech No thank you.

Anonymous

Anonymous Mon 11 Jan 2021 15:28:12 No.12568746 Report

Quoted By:

>>12564901
That's like asking what the use for negative numbers is. It's an extension of what was already present. Yes, of course they have purpose. Just Google it to find some examples, they're numerous

Anonymous

Anonymous Mon 11 Jan 2021 15:32:18 No.12568761 Report

Quoted By:

>>12564922
you can, and there are algebraic structures in division is always possible (quasigroups, loops, division rings included) but these don't turn out to be nearly as useful as complex numbers are.

Anonymous

Anonymous Mon 11 Jan 2021 15:42:02 No.12568795 Report

Quoted By:

>>12568678
that's not the point of the disccusion. my impression is that the person I'm responding to is completely ok with "R^2 equipped with an extra operation", but not with "complex numbers". that's a total misunderstanding.

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