IMC 2024 · Problem 1

Day 131st IMC · Blagoevgrad, Bulgaria

Statement

Determine all pairs $(a, b) \in \mathbb{C} \times \mathbb{C}$ satisfying

|a| = |b| = 1 \quad \text{and} \quad a + b + a\bar{b} \in \mathbb{R}.

Hidden so you can work on the problem first.

Proposed by Mike Daas, Universiteit Leiden.