Question

1+z+z^2+....+z^n=0
Va rog! :(

Answer 1

$1+z+z^2+\ldots+z^n=1\cdot\dfrac{z^{n+1}-1}{z-1}=0\Rightarrow z^{n+1}=1\to\\\to z_k=cos\left(\dfrac{2k\pi}{n+1}\right)+i\cdot sin\left(\dfrac{2k\pi}{n+1}\right),\;unde\;k\;ia\;valori\;de\;la\;0\;la\;n.$

Green eyes.