What happens here /sci/? inb4 [math]i+1[/math]

>>8769851
looks more like 2/3 + 2i/3 to me

Are you asking for the 45 degree rotational value for the complex plane?

>>8769858
No, I'm not asking for the root of unity that gives you the 45 degrees of [math] i [/math]

I'm asking about what happens there without using [math] i [/math], i.e what's the complex number of the 3rd dimension that's not a quaternion

>>8769851
The only real division algebras are of dimension 1 (reals), 2 (complexes), 4 (quaternions), 8 (octonions).

There is no dimension 3 analog

>>8769924
But that's the problem - quaternions and octonions both use [math] i [/math], while in contrast both the reals and complex are separate entities. So therefor we can conclude that going a dimension above should result in a separate division that

>1) Doesn't include anything from those below
>2) Is independently representable by its own number

But that's not the case as we're either simply warping the 2d plane itself to achieve a rotation, or simply include another one perpendicular to it. It's basically like adding an additional real number line to the Y axis to pretend that we have a complex number

What I'm trying to say is that regardless of how many dimensions there are above the 2nd, they should have their own separate representation like the other two, except they currently don't, and we're forced to glue two number lines of a dimension below to achieve it.

Are complex numbers only used over matrices for rotations?

>>8769945
What?
how are complex numbers and real numbers completely separate entities? They both use real numbers. All four of them have a real component. And why should the complex numbers have a completely separate element that isn't real? That's just completely retarded. How would you define this separate element? By an imaginary number? Imaginary numbers are defined in relation to real numbers, how exactly would you exclude the real numbers from the complex plane? I just don't get what you're complaining about or trying to say.

>>8769851
[math]\frac{i+1}{\sqrt{2}}[/math]

>>8769851
[math]e^{i\pi/4}=cos(\pi/4)+isin(\pi/4)=i/\sqrt{2}+1/\sqrt{2}[/math]

>>8769945
I know what you're trying to say, but unfortunately, you have no idea what you're talking about.

>>8770732
>>8770740
Literally intro complex variables shit

>>8769879
>>8769945
You can cross product [math]\mathbb{C}\times\mathbb{R}[/math] and there are plenty of coordinates (e^i pi/4,x) which project that way onto the complex plane. But whats the point? What youre saying is gibberish

I dropped out of high school and even i'm not this brainlet

>>8770740
>uses Latex
> doesn't use fractions
> wat