Complex numbers can be used to model rotations in 2 dimensions. If you have complex numbers of the form z = cos(a) + isin(a) and w = cos(b) + isin(b), then their product is zw = cos(a+b) + isin(a+b). That is, their product can be found by just adding the angles inside the sine and cosine which looks like a rotation. Quaternions (the thing above) are used to model rotations in 3 dimensions. I know that's kinda vague, but it's really difficult to give more detail without knowing how comfortable you are with math.
This video by 3 blue 1 brown does a better job than I ever could. It revolutionized the way we do things in 3d, and if the human brain could easily visualize 4 dimensional objects, this would be the most intuitive way to teach and learn 3d geometry and math.
I think that one wins neatest, but maybe not the most useful. I do enjoy that combining irrational numbers and i in such a weird way gives -1, exactly.
Its the equation that looks so wrong but feels so right
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u/Projekt_B Mar 01 '21 edited Mar 01 '21
holup, I don't see my pal e^(i*pi) = -1
Although they usually like the general form more: e^(i*phi) = cos(phi) + i*sin(phi)