Derivative of squared norm of a complex function Assuming $f(x)$ is a complex function, its squared norm is defined as $$|f(x)|^2 = f(x) . f^*(x)$$

What is derivate of $|f(x)| ^ 2$?
For a complex variable a, |a|^2 derivative exist only at zero. Try evaluating at x_0+i*y_0 not zero. Approach from y=y_0 and you get 2*x_0 but approach from x=x_0 and you get -2*y_0*i. And at zero you get limit r^2 over re^(thetai) that go to zero.
For a complex variable a, |a|^2 derivative exist only at zero. Try evaluating at x_0+i*y_0 not zero. Approach from y=y_0 and you get 2*x_0 but approach from x=x_0 and you get -2*y_0*i. And at zero you get limit r^2 over re^(thetai) that go to zero.