Problem 1. Determine all pairs \(\displaystyle (a,b) \in \mathbb{C} \times \mathbb{C}\) satisfying
\(\displaystyle |a| = |b| = 1 \quad \text{and} \quad a + b + a\overline{b} \in \mathbb{R}. \)
Mike Daas, Universiteit Leiden
Hint Solution
