$$z_1= 4\sqrt{2}-i4\sqrt{2}$$
$$z_2= \cos{135^\circ} +i\sin{135^\circ}$$
Find all the complex numbers $z$ that fulfill the following equation: $${z_1\over \overline{z_2}} = z^3$$
be aware that $z_2$ in the last description is with an overline.
Solve ${z_1/\overline{z_2}} = z^3$
Find one $z_0$ and the other two are $z_o\omega, z_0\omega^2$, where $\omega=-\dfrac{1}{2}+\dfrac{\sqrt{3}}{2}i$
*$z_1=8(\cos(7\pi/4)+i\sin(7\pi/4)),\bar{z_2}=\cos(-3\pi/4)+i\sin(-3\pi/4)$
$z_1/\bar{z_2}=8(\cos(5\pi/2)+i\sin(5\pi/2))$
so one solution will be $z_0=2(\cos(5\pi/6)+i\sin(5\pi/6))=-\sqrt{3}+i$