Answer
$2cis67.5^\circ,2cis157.5^\circ,2cis247.5^\circ,2cis337.5^\circ$
Work Step by Step
1. Let $z=-16i=16(-i)=2^4(cos270^\circ+i\ sin270^\circ)$, we have the fourth roots as
$z_k=\sqrt[4] z=2(cos(\frac{360k+270}{4})^\circ+i\ sin(\frac{360k+270}{4})^\circ)$ where $k=0,1,2,3$
2. For $k=0$, $z_0=2(cos67.5^\circ+i\ sin67.5^\circ)=2cis67.5^\circ$
3. For $k=1$, $z_1=2(cos157.5^\circ+i\ sin157.5^\circ)=2cis157.5^\circ$
4. For $k=2$, $z_2=2(cos247.5^\circ+i\ sin247.5^\circ)=2cis247.5^\circ$
5. For $k=3$, $z_3=2(cos337.5^\circ+i\ sin337.5^\circ)=2cis337.5^\circ$
