Inegalitate cu numere complexe

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mihai++
Bernoulli
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Joined: Wed Nov 28, 2007 8:08 pm
Location: Focsani

Inegalitate cu numere complexe

Post by mihai++ »

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:
\( \ \sum_{1\leq j<k\leq n} |z-z_k||z-z_j|\geq \max(1,|z|^2)\cdot C_n^2. \)
n-ar fi rau sa fie bine :)
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