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A comment on Quantum Physics Falls Apart Without Imaginary Numbers. Parent comment
y = cos(pi * (x-1)). No complex numbers needed.
Yes, you can make a 3-D spiral / helix by mapping from R to C, but (a) that's only when your domain is R; ignoring when the domain is C.
The spiral doesn't help you with a simple task like solving this: 0 = x^2 +1
A helix is a time-based view of drawing a circle, in the plane.
Your favorite use of complex numbers isn't the only use of complex numbers.
https://brilliant.org/wiki/complex-numbers-in-geometry/
https://web.evanchen.cc/handouts/cmplx/en-cmplx.pdf
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y = cos(pi * (x-1)). No complex numbers needed.
Yes, you can make a 3-D spiral / helix by mapping from R to C, but (a) that's only when your domain is R; ignoring when the domain is C.
The spiral doesn't help you with a simple task like solving this: 0 = x^2 +1
A helix is a time-based view of drawing a circle, in the plane.
Your favorite use of complex numbers isn't the only use of complex numbers.
https://brilliant.org/wiki/complex-numbers-in-geometry/
https://web.evanchen.cc/handouts/cmplx/en-cmplx.pdf