The use of imaginary and complex values comes up in many physics and engineering derivations. I have a question about that: Is the use of complex numbers simply to make the process of derivation easier, or is it an essential ingredient, without which it would be impossible to derive some results?
I can identify two different settings where the answer may be different:
It doesn't look like it is mandatory for results in Newtonian mechanics, General Relativity and classical electrodynamics.
Can we say the same thing about quantum mechanics either way for sure?
Could this be a difference in quantum mechanics over the classical picture?
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