Do imaginary numbers in quantum mechanics do anything different than, say, a regular 3D coordinate system? Why do they show up in e.g the Schrödinger Equation? Is it because "i" can model waves and circular motion (e^i(pi) iirc)? If so, do complex and imaginary values do anything different than a sine or cosine function? Sorry if this sounds like alot, I'm just confused why imaginary quantities are showing up in physics.
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