Problem

Source: Romania National Olympiad 2022

Tags: complex numbers, romania, inequalities



Let $z_1$ and $z_2$ be complex numbers. Prove that \[|z_1+z_2|+|z_1-z_2|\leqslant |z_1|+|z_2|+\max\{|z_1|,|z_2|\}.\]Vlad Cerbu and Sorin Rădulescu