> A simpler preliminary question would be, why are complex numbers present in non quantum wave mechanics I'm not sure there's anything deep here. Imaginary exp

> A simpler preliminary question would be, why are complex numbers present in non quantum wave mechanics I'm not sure there's anything deep here. Imaginary exponentials contain sines and cosines and so are the solution to a lot of differential equations, even in the complex solutions have no physical interpretations. See e.g. the case of electromagnetism.