Question

$$(-1+i\sqrt{3})^{4}(-1-i\sqrt{3})^{5}=512w^{2}$$

Solve for w

$w=e^{\frac{5\pi i}{3}}\approx 0.5-0.866025404i$
$w=e^{\frac{2\pi i}{3}}\approx -0.5+0.866025404i$