Electromagnetism concerns movement of what appear to be moving circles. If you roll a circle with a pen marker it draws a sine or cosine curve. If you try to draw the spiral of a light wave you get perpendicular sine and cosine curves. Light is electromagnetic radiation and in turn both electricity and magnetism are fundamentally connected forces.

there is no "spiral of a light wave" lol. If anything, I'd think of transversal movement. Ironically I cannot say that nobody has ever seen a photon. But nobody has ever seen an electron. There could be a model in which electrons move transversal (at mm/s), mediated by photons, but I have not looked that closely into it. It's not part of the usual theories.

if you attach a pen to a hoop and move the hoop along a wall, you do not get a wave, you get (edit: what looks like but isn't) sharp discontinuity where the pen touches the ground (https://google.com/search?q=cos%28x-sin%28x%29%29)

Circular polarized light is a spiral, at least in terms of how we normally draw the vector annotation.

You may say that AC has a lot to do with rotation.

EM is about rotating fields. Phase is very fundamentally connected with rotation. These are where complex numbers show up.