Anonymous at Thu, 7 Mar 2024 02:44:47 UTC No. 16060778

>>16060777
Imaginary numbers are your friend. They make your life so much easier when you are dealing with anything that is periodic.

This is especially true when you are looking at systems which respond to some brief input via a windowed exponential. Being able to write it as A(t)exp((a+bi)t) is pretty nice.

Anonymous at Thu, 7 Mar 2024 04:17:07 UTC No. 16060846

>>16060777
>be faggot math inventors
>realise you can't do anything without zero
>decide to change the rules in advanced math and allow nonexistent values as 0
This is proof that math is fake and gay, and predates i by a few thousand years

Anonymous at Thu, 7 Mar 2024 23:22:57 UTC No. 16062023

>>16060777
All of math is like this.
-----

Start with positive integers 1,2,3,...

Wait we don't additive inverses or an additive unit.

Create the integers.

Wait we don't have multiplicative inverses.

Create the rational numbers.

Wait we can't describe basic geometric proportions like the length of the hypotenuse of a triangle or solve a basic polynomial equation like x^2 - 2 = 0.

Create irrational algebraic numbers.

Wait we still can't describe basic geometric proportions like the circumference of a circle.

Create irrational transcendental numbers.

Wait we still can't solve x^2 + 1 = 0.

Create imaginary numbers.

Anonymous at Fri, 8 Mar 2024 14:32:35 UTC No. 16062804

>>16062023
>can't solve x^2 + 1 = 0
not what inspired i.
what made the change was x^3 functions like
x^3-5x^2+5=0
which has 3 real solutions
but needs i to be solved algebraically

Anonymous at Fri, 8 Mar 2024 14:52:32 UTC No. 16062839

>>16060777
i is just an operator that means rotate your shit 90 degrees
It's not imaginary
Do it twice and you're facing the other way, i2 = -1

Anonymous at Fri, 8 Mar 2024 14:54:49 UTC No. 16062847

>>16060777
this again...
https://www.youtube.com/watch?v=cUzklzVXJwo
https://www.youtube.com/watch?v=qtIsYbYdzCI

Anonymous at Fri, 8 Mar 2024 14:55:51 UTC No. 16062850

>>16062839
>It's not imaginary
i'll never forgive descartes for this retarde nomenclature

Anonymous at Fri, 8 Mar 2024 16:08:17 UTC No. 16062952

Fuck complex numbers. Seriously, fuck this shit. I'm okay with math fags playing their abstract language games. Complex numbers are supposed to be a niche thought experiment or toy model, a silly factoid like "Btw did you know you can define square roots of negatives? Mathematicians did this once and it works out but was never useful in applications." This is how it should be. I vehemently disagree with complex numbers being fundamental to nature. I disagree with having to do math with complex numbers to understand quantum mechanics. It just doesn't feel right. Everything we can see is real, not complex. The reals should be the basis for all of physics. I fucking hated my complex analysis class.

Anonymous at Fri, 8 Mar 2024 16:09:18 UTC No. 16062955

>>16062952
filtered

Anonymous at Fri, 8 Mar 2024 16:21:04 UTC No. 16062976

>>16062952
ALSO FUCK ZERO! FUCK THIS SHIT! IT'S THE DEVILS NUMBER! HOW CAN YOU ADD NOTHING TO SOMETHING AND GET TEN TIMES THE AMOUNT! IT'S WITCH CRAFT! HOW IS ZERO SUPPOSED TO BE A NUMBER IF YOU CAN'T EVEN DIVIDE BY IT!? FUCK THIS SHIT! SATANIC ARAB LIES!

Anonymous at Fri, 8 Mar 2024 16:34:07 UTC No. 16062993

>>16062952
anon... >>16062847

Anonymous at Fri, 8 Mar 2024 16:37:43 UTC No. 16063004

>>16062976
>HOW CAN YOU ADD NOTHING TO SOMETHING AND GET TEN TIMES THE AMOUNT
add?, do you mean wring first 1 which is one and then a dding a zero to its right making 10 which is ten?, do yo comprehend what positional notation is?

🗑️ Anonymous at Fri, 8 Mar 2024 16:45:47 UTC No. 16063022

>>16063004
I AM SORRY. I MEANT MULTIPLY! BETTER!?

Anonymous at Fri, 8 Mar 2024 16:46:53 UTC No. 16063026

>>16062976
Isn't zero the neutralization of all and not necessarily the nothing but more the controlled center.

Anonymous at Fri, 8 Mar 2024 16:50:27 UTC No. 16063032

>>16063026
If 0 is nothing, how can you have -1? What's that? - 1 nothing?

Anonymous at Fri, 8 Mar 2024 16:54:19 UTC No. 16063038

>>16060777
Trips prove this is fact.

OP, you're right, mathematicians are simply making things up as they go along. I can guarantee that anyone on this board can create a fundamentally groundbreaking discovery in mathematics given enough time.

These concepts have helped us get to the moon and such, so they're not entirely useless.

I think computer math dealing with 1's and 0's are better but has a larger learning curve. Our ideas about math are restricted to things like how many fingers we have and then we correct from there.

Anonymous at Fri, 8 Mar 2024 16:57:40 UTC No. 16063048

>>16063038
>I can guarantee that anyone on this board can create a fundamentally groundbreaking discovery in mathematics given enough time.
are you calling us monkeys, anon?

Anonymous at Fri, 8 Mar 2024 16:58:26 UTC No. 16063049

>open qm textbook
>these operators have to be hermitian because we can't cope with complex spectra

🗑️ Anonymous at Fri, 8 Mar 2024 17:02:48 UTC No. 16063065

>>16060777
Fuck off you idiot.

Anonymous at Fri, 8 Mar 2024 17:03:07 UTC No. 16063067

>>16063032
-1 is obviously an apple shaped hole in which other apples vanish when you add it to your pile.

🗑️ Anonymous at Fri, 8 Mar 2024 17:13:51 UTC No. 16063097

>>16063032
That is debt. The US dollar is debt. All morons like you must be eradicated or civilization will collapse.

🗑️ Anonymous at Fri, 8 Mar 2024 17:17:53 UTC No. 16063107

>>16062952
LMAO, you are the reason why academia is a shit show.

Anonymous at Fri, 8 Mar 2024 17:18:19 UTC No. 16063109

>>16063097
Easier to do with neutralization than cancellation.

🗑️ Anonymous at Fri, 8 Mar 2024 17:20:28 UTC No. 16063113

>>16062850
There is a word in the Xhosa language that means side: icala, i is icala.

Anonymous at Fri, 8 Mar 2024 17:25:09 UTC No. 16063125

>>16063113
mh, i can see that, i does fit with what gauss wanted to name them, fair enough

Anonymous at Fri, 8 Mar 2024 19:11:09 UTC No. 16063309

>>16060777
you stupid faggots never get the definition of i right.
it's [math]i^2 \equiv -1[/math] dumbass. using a root as a "definition" is ambiguous, as i could be 2 different numbers

Anonymous at Fri, 8 Mar 2024 21:28:16 UTC No. 16063596

>>16063309
>as i could be 2 different numbers
?, -i*-i=/=-1?, im sure it was i*-i=1

Anonymous at Fri, 8 Mar 2024 21:31:39 UTC No. 16063604

>>16060777
why do incels paddle the same fake story about the emergence of complex numbers?
>Decide to change the rules
exactly 0 rules have been changed, complex numbers are a different set than reals

Anonymous at Fri, 8 Mar 2024 21:58:18 UTC No. 16063651

>>16063596
both [math]-i \dot{} -i = -1[/math] and [math]i \dot{} i = -1[/math]

Anonymous at Fri, 8 Mar 2024 23:39:15 UTC No. 16063826

>>16063651
ah, ok, though so

Anonymous at Fri, 8 Mar 2024 23:41:16 UTC No. 16063828

>>16063604
For every number x we have x^2 > 0. That's a rule. Introducing "imaginary numbers" changes that rule. Next time learn your math before posting, kid.

Anonymous at Sat, 9 Mar 2024 06:41:32 UTC No. 16064520

>>16063828
>For every number x we have x^2 > 0
so 0^2 > 0 ?
interesting math faggot lmao
>That's a rule
it's a property of certain types of number, it's not a rule retard lmao

Anonymous at Sat, 9 Mar 2024 07:43:32 UTC No. 16064581

>>16062952
You would like Morris Kline and Norman Wildberger. All math has to be constructed and related to realities (even if those realities are just "I like the gay puzzles it lets me do," at least you are remaining conscious of WHAT it is exactly that you are constructing).

I think of imaginary and complex numbers like this: they are parasitic on real things, and whenever they "do" anything real, it's always because they "cancelled themselves back out" into the real something they were derived from to begin with. They could even be expressed in a more intuitive "real" way, but by fudging their reality WITHIN the notional realm of mathematics in those "in-between" moments, where they are just bridging between two real moments, time is sometimes saved.

They are like shadows or reflections off of real things capable of being intuited. Same with all abstract mathematics.

Anonymous at Sat, 9 Mar 2024 07:50:17 UTC No. 16064594

>>16062952
>walk along the sidewalk
>find a pole standing in the middle of the path
>your friend just gets around it by briefly leaving the sidewalk
>you remain stuck seething telling him that leaving the path is prohibited and you must go over the obstacle by climbing over it or some shit
this is you

Anonymous at Sat, 9 Mar 2024 08:10:20 UTC No. 16064619

Nigga you retarded.

Anonymous at Sat, 9 Mar 2024 08:54:13 UTC No. 16064678

>>16060777
It's easier to accept imaginary numbers when you realize they're just placeholders for intermediate results and never a final, usable answer for anything.

Anonymous at Sat, 9 Mar 2024 09:09:45 UTC No. 16064704

https://www.youtube.com/watch?v=60z_hpEAtD8

Anonymous at Sat, 9 Mar 2024 10:32:10 UTC No. 16064790

What if I told you that - just rotates a number 180 degrees around 0?

Anonymous at Sat, 9 Mar 2024 12:53:19 UTC No. 16064882

>>16062952
Complex numbers aren't fundamental to nature (only [math]\Z \ {0}[/math] is. Everything else derives from that), but you are an unbelievable brainlet if you don't understand their use for technical applications. Just how would you model phases and oscillations in a simple way without i? I mean you don't have yo reply, since you obviously don't even know what I am referring to.

Anonymous at Sat, 9 Mar 2024 13:02:11 UTC No. 16064892

>>16064882
>how would you model phases and oscillations
Sine and cosine. You're a braindead pajeet whose highest achievement is to regurgitate some formula involving complex numbers for an exam, and you clearly don't even know simple trigonometry. Embarrassing.

Anonymous at Sat, 9 Mar 2024 13:35:55 UTC No. 16064917

>>16060778
Why can't we just use trig functions in the same places? They are also periodic in a predictable way

Anonymous at Sat, 9 Mar 2024 13:51:55 UTC No. 16064932

>>16062952
You went through an entire complex analysis but maybe you should have taken a foundations course. Or intro philosophy of math. Who cares if it isn't a "real" thing. It just works anon. All sorts of abstract objects don't actually exist, does that mean you shouldn't be allowed to imagine them?

Anonymous at Sat, 9 Mar 2024 13:52:49 UTC No. 16064933

>>16064917
Imaginary numbers are how you figure out the right trig functions to use in many cases.

This is especially true when you've got something like "windowed oscillation" where you have a signal which is decaying with time in amplitude while oscillating in frequency.

Anonymous at Sat, 9 Mar 2024 13:54:43 UTC No. 16064938

>>16063032
Its just 1 but going in the other direction

Anonymous at Sat, 9 Mar 2024 14:00:35 UTC No. 16064949

>>16064933
Ok. I'll just look for an example i guess. I don't really understand. But your dubs are convincing

Anonymous at Sat, 9 Mar 2024 16:00:01 UTC No. 16065098

>>16064932
What makes complex numbers so ugly is the fact that they are not compatible with geometry. Nobody can imagine, let alone visualize a complex-valued function.

Anonymous at Sat, 9 Mar 2024 17:24:52 UTC No. 16065183

>>16064949
Take a look at a signals and systems book. You can find a PDF of Lathi's Signal Processing & Linear Systems online and it's all about using Fourier representations of periodic signals (and Laplace when you get to signals with decaying amplitude). That's all complex variables to represent signals that would be very cumbersome to represent exactly solely through real sinusoidal functions relative to their complex exponential representation.

Anonymous at Sat, 9 Mar 2024 17:31:45 UTC No. 16065189

>>16062952
Nigga it is just the cartesian plane with a function that when taking 2 vectors multiplies the lengths and rotates. Is rotation imaginary? Cuz that’s all the complex numbers are.

Anonymous at Sat, 9 Mar 2024 17:49:57 UTC No. 16065209

>>16065098
Believe me, if you work with it for enough time, you can easily visualize it without pen and paper.

But it's right to say that the discover of imaginary numbers was the first step to realize that it cant be associated with an entity in the physical world like any numbers before.

And imaginary numbers are totally compatible with geometry in the form a+ib (vector form) or a.e^(ib) (polar form) to add or multiply vectors.

Check "geometry with de Moivre's formula".

Anonymous at Sat, 9 Mar 2024 19:32:56 UTC No. 16065356

>>16064581
>*all of that*
no wonder you like those retards

Anonymous at Sat, 9 Mar 2024 19:33:58 UTC No. 16065357

>>16064678
worng

Anonymous at Sat, 9 Mar 2024 19:35:00 UTC No. 16065360

>>16064882
>Complex numbers aren't fundamental to nature
but they are

Anonymous at Sat, 9 Mar 2024 19:38:16 UTC No. 16065366

>>16065209
i think he's talking about how a complex function need a 4d space to be fully visualized, my counter point to that would be this guy's 4d golf game:
https://www.youtube.com/playlist?list=PLh9DXIT3m6N4GygehtlHl0ukgrgPJZteI

Anonymous at Sun, 10 Mar 2024 01:26:09 UTC No. 16065837

>>16065360
This is so fucking cringe. Talking about anything as "fundamental to nature" doesn't even mean anything, so why even say it, or worse yet, argue about it?