Question 79
Let $g : \mathbb{C} \rightarrow \mathbb{C}$ be a surjective function. Find all complex functions $f : \mathbb{C} \rightarrow \mathbb{C}$ such that for any two complex numbers $x, y$, we have:
$$
|g(x) + f(y)| = |f(x) + g(y)|.
$$
$$
|g(x) + f(y)| = |f(x) + g(y)|.
$$