Question

clasa 10: Sa se rezolve ecuatiile:  z la puterea a 6-a -i+1=0     Este ecuatie binoma iar solutiile sunt k=? si z indice k=? plzzz sa inteleg

Answer 1

$z^6=-1+i$

$|-1+i|=\sqrt2$

$-1+i\in cadr.II$

$arg(-1+i)=\pi-\dfrac{\pi}{4}=\dfrac{3\pi}{4}$

$z_k=2^{\frac{1}{12}}\left(cos\dfrac{\frac{3\pi}{4}+2k\pi}{6}+i\ sin\dfrac{\frac{3\pi}{4}+2k\pi}{6}\right);\ k\in\{0;1;2;3;4;5\}$