Problem

Source: Iran 2024 3rd round algebra exam P2

Tags: algebra, functional equation



A surjective function $g: \mathbb{C} \to \mathbb C$ is given. Find all functions $f: \mathbb{C} \to \mathbb C$ such that for all $x,y\in \mathbb C$ we have $$ |f(x)+g(y)| = | f(y) + g(x)|. $$ Proposed by Mojtaba Zare, Amirabbas Mohammadi