Intersectia a doua multimi de numere complexe

[Andrei Velicu]

Fie \( n\geq 3 \) un numar intreg si \( z=\cos\frac{2\pi}{n}+i\sin\frac{2\pi}{n} \). Consideram multimile \( A=\left\{1,z,z^2,\ldots,z^{n-1}\right\} \) si \( B=\left\{1, 1+z, 1+z+z^2,\ldots, 1+z+\cdots +z^{n-1}\right\} \). Sa se determine multimea \( A\cap B \).

Marcel Tena, Olimpiada Judeteana 2008