Complex Numbers Extension

[BonesYT]

I couldn't find an extension dedicated to complex numbers, you know... sqrt(-1) and stuff like that, so I made one. This is also my first extension, and it kinda works pretty well!

All features:

• Construct a complex number with real and/or imaginary component

• Get the real and imaginary components of that value

• Boolean to check if a number is real or not

• Addition, subtraction, multiplication, division and exponentiation. And modulo.

• Functions with single input, with extra: conjugate, flip, sign, atan2.

• Toggle between simple and advanced syntax, for perfomance reasons. Maybe simple mode is at least slightly faster.

Examples

1. Mandelbrot Set
2. Julia Set

[penta-quark-neutro]

Interesting, I also made one of the same thing, but for personal use. Your extension is quite good, but slow. It takes almost 2.57 seconds to exponentiate 1000000 complex numbers. Approximately 4 times slower than mine. I think you should optimize it.

[Kenay555]

Hi @BonesYT ! I may or may not made something similar (like, with more blocks and such...) see #2113 for more :D Anyways, I'm working on updating my extension, because it's wierd with every letter. Plus, I found how to implement Quaternions, and maybe have more optimization ideas for it, maybe too many... I liked how you tackled some problems in the file. But that's not why I am here.

I was recently told about your existence, and looks like your extension has more power than mine (altho I have more blocks >:D but that's not the point either). From mathematician to cool guy, wanna work together?

(or maybe we should call @penta-quark-neutro to see what optimizations he used!)

[penta-quark-neutro]

There are fairly simple ways to get better performance. In the case of my extension, I simply rewrote the operations to avoid classes or calling functions. Using vectors is very efficient, but I imagine that your extension should return a string. This is an example of a way to implement octonions and have them calculate quickly: "octa3(ar){const v1=ar.a,v2=ar.b;return [(v1[0]*v2[0])-(v1[1]*v2[1])-(v1[2]*v2[2])-(v1[3]*v2[3])-(v1[4]*v2[4])-(v1[5]*v2[5])-(v1[6]*v2[6])-(v1[7]*v2[7]) ,(v1[0]*v2[1])+(v1[1]*v2[0])-(v1[2]*v2[3])+(v1[3]*v2[2])-(v1[4]*v2[5])+(v1[5]*v2[4])+(v1[6]*v2[7])-(v1[7]*v2[6]) ,(v1[0]*v2[2])+(v1[1]*v2[3])+(v1[2]*v2[0])-(v1[3]*v2[1])-(v1[4]*v2[6])-(v1[5]*v2[7])+(v1[6]*v2[4])+(v1[7]*v2[5]) ,(v1[0]*v2[3])-(v1[1]*v2[2])+(v1[2]*v2[1])+(v1[3]*v2[0])-(v1[4]*v2[7])+(v1[5]*v2[6])-(v1[6]*v2[5])+(v1[7]*v2[4]), (v1[0]*v2[4])+(v1[1]*v2[5])+(v1[2]*v2[6])+(v1[3]*v2[7])+(v1[4]*v2[0])-(v1[5]*v2[1])-(v1[6]*v2[2])-(v1[7]*v2[3]), (v1[0]*v2[5])-(v1[1]*v2[4])+(v1[2]*v2[7])-(v1[3]*v2[6])+(v1[4]*v2[1])+(v1[5]*v2[0])+(v1[6]*v2[3])-(v1[7]*v2[2]),( v1[0]*v2[6])-(v1[1]*v2[7])-(v1[2]*v2[4])+(v1[3]*v2[5])+(v1[4]*v2[2])-(v1[5]*v2[3])+(v1[6]*v2[0])+(v1[7]*v2[1]),( v1[0]*v2[7])+(v1[1]*v2[6])-(v1[2]*v2[5])-(v1[3]*v2[4])+(v1[4]*v2[3])+(v1[5]*v2[2])-(v1[6]*v2[1])+(v1[7]*v2[0])]}" Avoid calling functions and creating intermediate steps, avoid creating more variables than necessary, and chaining uses more resources and should be minimized. Even the example I provided could be optimized further, but I'm currently working on an object extension and adding sedenions to my vector extension. Good luck.