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function in C(2)

Source: Nicolae Coculescu contest

November 19, 2013
functionalgebra proposedalgebra

Problem Statement

Let w∈C∖Rw\in \mathbb{C}\setminus \mathbb{R}, ∣w∣≠1|w|\neq 1. Prove that f ⁣:C→Cf\colon \mathbb{C} \to \mathbb{C}, given by f(z)=z+wz‾f(z)= z+w\overline{z}, is a bijection, and find its inverse.
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