Solution (source code)

= Solution

Write $-8i=8e^{-i\pi/2}$. The three distinct <complex roots> are $z=2e^{i(-\pi/6+2k\pi/3)}$, $k=0,1,2$. In Cartesian form,
$$
\boxed{z=\sqrt3-i,\quad 2i,\quad-\sqrt3-i.}
$$