Trei numere complexe

[Mateescu Constantin]

Sa se determine \( z_1 \), \( z_2 \), \( z_3\in\mathbb{C} \) pentru care: \( |z_1|=|z_2|=|z_3|=1 \) si \( z_1^2+z_2^2+z_3^2=0 \) .

[Marius Mainea]

\( \{z_1,z_2,z_3\}=\{\alpha,\pm\alpha\epsilon,\pm\alpha\epsilon^2\} \) unde \( |\alpha|=1 \) si \( \epsilon^3=1 \) , \( \epsilon\neq 1 \)