MathDB

Equation with complex numbers on the unit circle

Source: IMC 2024, Problem 1

August 7, 2024

complex numbers

Problem Statement

Determine all pairs

(a,b) \in \mathbb{C} \times \mathbb{C}

of complex numbers satisfying

|a|=|b|=1

and

a+b+a\overline{b} \in \mathbb{R}