Anonymous at Fri, 31 May 2024 19:00:42 UTC No. 16202849

>>16202841
Is more than an ordered pair. An hyperbolic number is also more than an ordered pair, where j squared is 1, and j is not 1.

Anonymous at Fri, 31 May 2024 19:26:30 UTC No. 16202878

>>16202849
>Is more than an ordered pair
No it's not
>An hyperbolic number is also more than an ordered pair
No its not
>where j squared is 1
But it isn't.
[math]j*j = 1[/math], where star is defined as [math](a,b) * (c,d) = (ac+bd, ad+bc)[/math]

Anonymous at Fri, 31 May 2024 21:37:28 UTC No. 16203035

>>16202841
>Why do they teach complex numbers in such a weird and confusing way?
Because the numbers are so "real" that we don't even know what they are.

>Why not just say that a complex number is an ordered pair of real numbers? Is it to make normies hate math and think it's all made up and gay?
Mathematicians needs quantities, how else are they going to do math?

Anonymous at Fri, 31 May 2024 21:41:47 UTC No. 16203037

>>16202841
Cause that's the defining property of i. As a random person on the street to make up the rules to add (a,b) and (c,d), then ask them to make up rules to multiply them. You really think people are going to multiply them like complex numbers?

Anonymous at Fri, 31 May 2024 21:43:02 UTC No. 16203041

>>16202878
feels more made up and gay than j^2 =1 or i^2 = -1

Anonymous at Fri, 31 May 2024 23:29:26 UTC No. 16203212

>>16202841
>Here's i and its square is -1 because I say so
you had one job, and you already fucked it up, dumbass
the definition of the complex unit is [math]i^2 \equiv -1 \equiv[/math]

Anonymous at Sat, 1 Jun 2024 00:04:13 UTC No. 16203253

>>16202841
Hey kid, nice complex numbers you have there. Would be a shame if someone broke your mathematics. Heh, nothing personal.
[eqn]
1=\sqrt{(-1)*(-1)}=\sqrt{-1}*\sqrt{-1}=i*i=i^2=-1
[/eqn]

Anonymous at Sat, 1 Jun 2024 00:25:03 UTC No. 16203282

>>16202878
You are a complete imbecile idiot.

Anonymous at Sat, 1 Jun 2024 00:43:17 UTC No. 16203319

>>16203041
That meatbot is contradicting himself. The notation using ordered pairs is just another way to express the same idea, but without using i and j. However is necessary to define how to do operations like multiplication, therefore an ordered pair is not enough. Different definitions for those operations result in complex numbers, split-complex numbers, or anything else that may or may not be of practical value.

Anonymous at Sat, 1 Jun 2024 00:49:11 UTC No. 16203327

>>16203253
The first equality is wrong. Square roots have a negative and a positive value. You can't just pick whatever you want and forget the other like that.

Anonymous at Sat, 1 Jun 2024 01:03:56 UTC No. 16203344

>>16203327
in that case, the big-dicked anon chose one of the cases to demonstrate that using square root in the definition is turbo-brainlet-tier

Anonymous at Sat, 1 Jun 2024 02:30:22 UTC No. 16203444

>>16203327
>Square roots have a negative and a positive value.
nope
[math]
\sqrt {x^2} \ne \pm x, \quad \sqrt {x^2} = \left | x \right |
[/math]

Anonymous at Sat, 1 Jun 2024 02:39:40 UTC No. 16203458

>>16202841
If you’re doing actual science (physics/engineering) you can safely ignore “”””complex numbers”””” entirely. Any equations that use complex numbers can be rewritten without them. It’s just schizo bullshit that mathniggers made up. If you would like to prove me wrong, simply show me a picture of i apples.

Anonymous at Sat, 1 Jun 2024 02:41:19 UTC No. 16203460

>>16203458
>Being this wrong.
You're more likely to work with complex numbers in physics and engineering than in mathematics.

Anonymous at Sat, 1 Jun 2024 02:43:29 UTC No. 16203462

>>16203460
>he doesn't study complex analysis

Anonymous at Sat, 1 Jun 2024 02:43:48 UTC No. 16203463

>>16203460
Read my post nigger

Anonymous at Sat, 1 Jun 2024 03:34:21 UTC No. 16203519

>>16203460
Show the fucking apples you absolute retard

Anonymous at Sat, 1 Jun 2024 03:45:39 UTC No. 16203523

>>16202841
> Why do they teach X in such a weird and confusing way?
>Why not just say Y?
The answer, just like 95% of cases, is that they actually do say Y, and the thing you’re complaining about is not confusing but important motivation for the concept im the first place

Anonymous at Sat, 1 Jun 2024 03:46:47 UTC No. 16203526

>>16203519
show me any number. i've never actually seen one in the flesh.

Anonymous at Sat, 1 Jun 2024 03:53:26 UTC No. 16203536

>>16203526
Number is metaphysical so people use tokens such as numerals,lines and apples to show Number, now show the fucking imaginary apples

Anonymous at Sat, 1 Jun 2024 04:37:29 UTC No. 16203603

>>16202841
they should just teach it in an algebraic manner
>>16202841
>Why not just say that a complex number is an ordered pair of real numbers?
because it's not

Anonymous at Sat, 1 Jun 2024 04:38:40 UTC No. 16203605

>>16203041
math is made up, it's not physical
physicality is a mere locus within mathematics

Anonymous at Sat, 1 Jun 2024 05:44:06 UTC No. 16203677

>>16203458
>>16203519
This. Yall fucking dumb for thinking bout negatives too. Wtf is a negative apple? Btw, did the greeks use negative numbers? NO, cuz they weren't stupid and knew that lines of negative length don't exist. Math like x+4=1 were said to have no solutions because they were "absurd". Fuck the chinese, bring in their stupid ass negatives for no reason. Take your gook shit outta here.

Anonymous at Sat, 1 Jun 2024 05:46:19 UTC No. 16203680

>>16202841
Normies need to realize real numbers are the problem not complex numbers.

Anonymous at Sat, 1 Jun 2024 05:48:18 UTC No. 16203681

>>16203677
>Yall
Stopped reading right there

Anonymous at Sat, 1 Jun 2024 05:53:19 UTC No. 16203684

>>16203681
Your mind probably stopped working a long time ago

Anonymous at Sat, 1 Jun 2024 06:17:06 UTC No. 16203710

>>16203684
true but only when I read African American vernacular

Anonymous at Sat, 1 Jun 2024 06:52:15 UTC No. 16203733

>>16202841
>Here's i and its square is -1 because I say so
that's not a complex number, that's just i

Anonymous at Sat, 1 Jun 2024 07:33:20 UTC No. 16203771

>>16203253
Your changing the order of operations between step 2 and 3

Anonymous at Sat, 1 Jun 2024 07:34:29 UTC No. 16203772

>>16203677
>burn those who proclaim irrational numbers exist

Anonymous at Sat, 1 Jun 2024 07:52:14 UTC No. 16203781

>>16203772
The mathematically approved method is to drown them.

🗑️ Anonymous at Sat, 1 Jun 2024 08:03:21 UTC No. 16203791

>>16202841

it should be in a Geometry class, because if you graph a complex number and multiply it by [math] i [7math] then it rotates that point (or line made from the origin to the point) by ninety degrees counter-clockwise.

Anonymous at Sat, 1 Jun 2024 08:05:31 UTC No. 16203793

>>16202841
it should be in a Geometry class, because if you graph a complex number and multiply it by [math] i [/math] then it rotates that point (or line made from the origin to the point) by ninety degrees counter-clockwise.

Anonymous at Sat, 1 Jun 2024 08:19:34 UTC No. 16203809

>>16203458
Unless youre a tard who doesn't believe in numbers, show me these first:
>0 apples
>-2 apples
>π apples

Anonymous at Sat, 1 Jun 2024 08:30:40 UTC No. 16203818

>>16203771
Are you claiming that (a*b)^n != a^n*b^n ?

Anonymous at Sat, 1 Jun 2024 10:09:01 UTC No. 16203927

>>16203037
That's not true lmao. i is not defined as [math]i^2 = -1[/math] it's defined as the ordered pair [math](0,1)[/math].
>you really think people would multiply them like that
What?? Who gives a fuck?

>>16203041
But it isn't tho. It's directly made up of things we already know.

>>16203212
>ESL

>>16203253
These types of "proofs" come directly from the retardation of [math]i = \sqrt-1[/math].

>>16203282
>no arguments

>>16203519
All you need to accept are natural numbers that's it. Whole, Rational, and Real numbers can be built up from there.

>>16203677
-n is the set of all pairs of natural numbers [math] (a,b)[/math] such that [math] a = b +n [/math].

Anonymous at Sat, 1 Jun 2024 10:21:29 UTC No. 16203934

[math]
\mathbb{C}=\left\{a\begin{pmatrix}
1& 0 \\
0 & 1 \\
\end{pmatrix}+b\begin{pmatrix}
0 & -1 \\
1 & 0 \\
\end{pmatrix} \Bigg| a,b \in \mathbb{R}\right\}

[/math]

Anonymous at Sat, 1 Jun 2024 10:23:44 UTC No. 16203936

>>16203934
Numbers aren’t vectors you stupid mathnigger

Anonymous at Sat, 1 Jun 2024 10:44:16 UTC No. 16203953

>>16203936
complex "number" are not numbers THO

Anonymous at Sat, 1 Jun 2024 11:05:14 UTC No. 16203969

>>16203953
Ok, thanks for admitting it finally

Anonymous at Sat, 1 Jun 2024 11:13:21 UTC No. 16203974

>>16203253
First equality and 3rd inequality are contradictory.
Choosing the branch of sqrt so that sqrt(1)=1 gives sqrt(x*(1/x)) = 1.
Letting x start at 1 keeps the inequality after splitting sqrt(1)*sqrt(1)=1*1=1.
Moving x to -1 from 1 around zero makes 1/x move to -1 around zero in the opposite direction.
at -1, x and 1/x will be on opposite branches of sqrt so you necessarily will get an i and a -i.

The "proof" is wrong at possibly two steps.
after the second "=" you might have the wrong branches for each sqrt
If the reader is smart enough to infer that they are on opposite branches after the second "=", the problem is after the 3rd "=" where they were incorrectly evaluated.

Anonymous at Sat, 1 Jun 2024 16:29:11 UTC No. 16204621

>>16203927
>i is not defined as i2=−1 it's defined as the ordered pair (0,1)
>they don't understand what a representation is, nor that representations can have more structure than what they are representing
complex numbers are a thing unto themselves

Anonymous at Sat, 1 Jun 2024 17:42:08 UTC No. 16204878

I don't buy the idea of "complex numbers." They don't exist. That's why they are called imaginary. What we have instead is a pair of real numbers on a Carteian plane and then certain rules are applied to them (for instance, how they are multiplied, how they are raised to a power, etc, etc).

Anonymous at Sat, 1 Jun 2024 23:07:43 UTC No. 16205327

>>16204878
>I don't buy the idea of "complex numbers."
What about the idea of "algebraic closure", do you "buy" that? The complex numbers are isomorphic to R^2, but they are not the same thing.

Anonymous at Sat, 1 Jun 2024 23:09:28 UTC No. 16205335

>>16203974
>the branch of sqrt
The square root function is single valued as this guy >>16203444 pointed out. That's not the problem with the proof.

Anonymous at Sun, 2 Jun 2024 04:45:27 UTC No. 16205779

>>16204878
>I don't buy
good thing they are free, so free in fact that they live rent free in your head

Anonymous at Sun, 2 Jun 2024 04:46:51 UTC No. 16205781

>>16204878
>That's why they are called imaginary.
nah,. they are called so because the "i think, therefore i am" nigga got filtered by them, which led him to call them so

🗑️ Anonymous at Sun, 2 Jun 2024 04:49:52 UTC No. 16205782

>>16205335
\sqrt {x^2} \ne \sqrt {x}

Anonymous at Sun, 2 Jun 2024 08:38:00 UTC No. 16205931

>>16205335
That definition is just specifying the branch.
If you want to just call that branch the square root function then you will still need to account for the other branch by using -sqrt

Anonymous at Sun, 2 Jun 2024 11:59:03 UTC No. 16206042

>>16202841
Best theory for them that I found is geometric algebra. You literally take two generic 2D vectors and multiply them without any fancy rule, just treat the components as you do for polynomials. From that (and a very simple axiom) it emerges everything you are familiar with namely the dot product, complex numbers, quaternions (with 3 components) and so on. It scales to n-dimensional vectors as well. Most important thing to take home is that complex numbers are NOT vectors in the traditional sense of having two real components. Instead they have a scalar component (the real part) and a bivector component (the imaginary part). That's why if you multiply by i (which is the unit bivector) it has the effect of 'rotating' the complex number by 90 degrees, because It has the multiplicative property of an object which is not a scalar or a real number.

Anonymous at Sun, 2 Jun 2024 13:17:25 UTC No. 16206104

>>16203710
>y'all
>AAV
I'm going to have to stop you right there, partner

Anonymous at Sun, 2 Jun 2024 13:20:43 UTC No. 16206110

>>16205781
True and real.
/thread

Anonymous at Sun, 2 Jun 2024 13:30:04 UTC No. 16206113

>>16203444
>>16205335
Wrong. The convention is to take only the positive value when the square root symbol is applied to a positive number.

Anonymous at Sun, 2 Jun 2024 19:28:26 UTC No. 16206565

>>16206042
complex numbers absolutely qualify as BOTH vectors AND scalars
they satisfy both the field and vectorspace axioms