real derivative of the magnitude of a complex function?

Dear all,

I'm new to these forums and not sure if this is in the right section, but calculus I think is the main part of the problem. So I'm trying to solve an optimization problem that requires me to take the (real) derivative of the magnitude of a complex function. Given a real vector and a function , how do I compute

I know that the complex derivative of the magnitude of a complex function is undefined, but the real derivative should be defined, right?

For those interested in the entire problem, the function is of the form

, where is a complex matrix and is a complex vector, but both are functions of a set of real inputs . is a constant vector. I'm fairly confident I can take the derivative of , but it's the magnitude that's giving me trouble.

Appreciate any help or insight. Thanks so much!