What do you mean by “require”? Complex numbers can be represented as a 2x2 matrix of real numbers (a scaled rotation around the origin), so transitively, that’s true for any equation involving complex numbers.
I don’t remember exactly since it’s been a while since I read it, but in Scott Aaronson’s Book “Quantum Computing Since Democritus” which is about how physics informs what’s computable. He talks about how the behaviour of quantum mechanics follows fairly straightforwardly from considering how probability works with complex numbers / bloch spheres. You can’t properly reproduce Bell’s Inequality without them I think?