Question

Exercițiul 3 subiect bac

Answer 1

$z^2+z+1=0$
z(z+1) = -1
$z+1 = \frac{-1}{z}$
$z+1+ \frac{1}{z} = 0 =\ \textgreater \ z + \frac{1}{z} = -1$

$z+ \frac{1}{z} = -1 | ^2$
$z^2 + \frac{1}{z^2} + 2 = 1$
$z^2 + \frac{1}{z^2} = -1$

$z^2 + \frac{1}{z^2} = -1 |^2$
$z^4 + \frac{1}{z^4} +2 = 1$
$z^4 + \frac{1}{z^4} = -1$