Inegalitate cu numere complexe
Posted: Wed Mar 25, 2009 1:36 pm
Fie \( n\geq3,n\in\mathbb{N} \) si \( z_1,z_2,\dots,z_n\in\mathbb{C},|z_k|=1,\forall k=\overline{1,n} \),
\( \sum z_k=\sum z_k^2=0 \). Sa se arate ca:
\( \ \sum_{1\leq j<k\leq n} |z-z_k||z-z_j|\geq \max(1,|z|^2)\cdot C_n^2. \)
\( \sum z_k=\sum z_k^2=0 \). Sa se arate ca:
\( \ \sum_{1\leq j<k\leq n} |z-z_k||z-z_j|\geq \max(1,|z|^2)\cdot C_n^2. \)