[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 103 KB, 361x502, fourier.jpg [View same] [iqdb] [saucenao] [google]
7271908 No.7271908 [Reply] [Original]

>mfw complex numbers aren't very complex at all

>> No.7271918

>>7271908
Really what's the point of working in n dimensional complex when you can just work in 2n dimensional real

What properties are not preserved in this identification

>> No.7271930

>>7271908

Was Fourier a fatso? Fuck him.

From now on, I'll fancy Mellin.

>> No.7271932

>>7271918
why do complex analysis when you can do 2n real analysis

>> No.7271933

>>7271932

Because you lose everything that makes the complex plane interesting, that is, the Laurent series and the Residue theorem, and everything associated with them.

>> No.7271948

>>7271933
>Residue Theorem
>not just an analogue of Stokes Theorem

>> No.7271952

>>7271948

Believing the former is just plane wrong.

>> No.7271958

>>7271918
Complex numbers are more amenable to having numbery things done to them. Many operations are defined on complex numbers that are not on a 2-vector.

>> No.7271967
File: 61 KB, 460x300, grothendieck_wizard.jpg [View same] [iqdb] [saucenao] [google]
7271967

OP, you're retarded. What you are asking is akin to, "why work with graphic matroids when we could just work with the graph?" or, "why use a group's representation when we can just write down its presentation?" While C^n is homeomorphic, isometric, and diffeomorphic to R^2n, the fact that C is the algebraic closure of R gives it a tonne of extra value. That fact alone has led to all of the intrinsic connections between number theory and complex analysis; while we could work with R^2n, we would then have to take time out of our schedule to jump back over to C^n. We work with matroids because the give us connections between linear algebra, field extensions, and combinatorics (ignore please the crime I committed in not mentioning that many matroids cannot be represented with a graph). And if we didn't work with groups via their representations, we wouldn't have glorious things like the modular group and Conway's monstrous moonshine.

>Grothendieck is disappoint

>> No.7271974

>>7271967
All that clever talk and you still assumed OP is >>7271918 for no reason at all.

>> No.7271977

>>7271974
Yeah, I think I wanted to reply to that dude.

What do you mean, "clever talk?" They cover the fact that C is the algebraic closure of R in any commutative algebra course you take. That person is being ignorant or trolling.