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Trei numere complexe
Posted: Thu Aug 27, 2009 8:55 pm
by Mateescu Constantin
Sa se determine \( z_1 \), \( z_2 \), \( z_3\in\mathbb{C} \) pentru care: \( |z_1|=|z_2|=|z_3|=1 \) si \( z_1^2+z_2^2+z_3^2=0 \) .
Posted: Thu Aug 27, 2009 11:08 pm
by Marius Mainea
\( \{z_1,z_2,z_3\}=\{\alpha,\pm\alpha\epsilon,\pm\alpha\epsilon^2\} \) unde \( |\alpha|=1 \) si \( \epsilon^3=1 \) , \( \epsilon\neq 1 \)