I have a problem in a demonstration where I have to do a derivative $\frac{df}{dc}$ of


where * denotes the complex conjugate.

In my demonstration the derivative $\frac{df}{dc}$is equal to 0. So I tried to solve it by applying the chain rule:


obtaining the result:


Unfortunately I should have obtained


Can you help me with this derivative of complex number? What am I doing wrongly?

  • 1
    $\begingroup$ $f=|y-cx|^2$ is not differentiable $\endgroup$
    – Raffaele
    Commented Dec 2, 2020 at 18:35

1 Answer 1


I'm confused; $c \mapsto \overline{c}$ is not analytic and $f=|y|+|cx|-\overline c \overline x y - cx\overline y$, so why should $f$ be complex-differentiable?


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