Find all complex numbers $z$ that satisfy equation $z^3=-8$
$z^3+8=0;$
$(z+2)(z^2-2z +2^2)=0;$
$z_1=-2;$
Solve quadratic equation:
$z_{2,3} = \dfrac{2\pm \sqrt{4-(4)2^2}}{2}$;
$z_{2,3}= \dfrac{2\pm i 2√3}{2}.$
$z^3+8=0;$
$(z+2)(z^2-2z +2^2)=0;$
$z_1=-2;$
Solve quadratic equation:
$z_{2,3} = \dfrac{2\pm \sqrt{4-(4)2^2}}{2}$;
$z_{2,3}= \dfrac{2\pm i 2√3}{2}.$