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Antonache Emanuel
Euclid
Posts: 37
Joined: Sat Feb 28, 2009 4:15 pm
Location: Targoviste, Dambovita

Shortlist 13

Post by Antonache Emanuel »

Fie \( z_1,z_2,...,z_n, n\ge4 \), numere complexe (nu neaparat diferite), pentru care:
\( |z_1|+|z_2|+...+|z_n|=1 \).Demostrati ca se pot alege unele dintre acestea pentru care modulul sumei este strict mai mare decat \( \frac{1}{4} \).
Valentin Vornicu, Shortlist 2003
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Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

aici
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