Inegalitate cu numere complexe

Mateescu Constantin · Post by **Mateescu Constantin** » Sun May 17, 2009 3:56 pm

Daca \( z_1,\ z_2,\ z_3\in \mathbb{C} \) sunt astfel incat \( z_1+z_2+z_3\neq 0,\ z_1^{2}+z_2^{2}+z_3^{2}=0 \) si \( |z_1|=|z_2|=|z_3| \), atunci \( |z_1^{3}+z_2^{3}+z_3^{3}|\leq 7 \).

Marius Mainea · Post by **Marius Mainea** » Thu May 28, 2009 12:15 pm

\( z_1=2 \), \( z_2=2(\cos \frac{\pi}{3}+i\sin \frac{\pi}{3}) \), \( z_3=2(\cos \frac{2\pi}{3}+i\sin \frac{2\pi}{3}) \) nu verifica.

Nu cumva modulele sunt egale cu 1?

Asa e enuntul in gazeta.

Insa concluzia devine evidenta.....?...?...

Mateescu Constantin · Post by **Mateescu Constantin** » Thu May 28, 2009 1:23 pm

Este problema 22809 din G.M 5-6/1993