Answer
$\color{blue}{8\ \text{cis}\ 270^\circ,\ 8\ \text{cis}\ 3\pi/2}$
Work Step by Step
$z=-8i = 0 -8i = x+iy \implies x=0, y=-8$
$\Huge\cdot$ modulus: $\quad r = \sqrt{x^2+y^2} = \sqrt{0^2+(-8)^2}= \sqrt{64} = 8$
$\Huge\cdot$ argument: $\quad \tan\theta=y/x=-8/0,\ \text{DNE};\ \sin\theta \lt 0 \implies \theta = 270^\circ \equiv 3\pi/2$ (smallest positive real angle $\theta$ from $+x$-axis to graph of $z$)
$\begin{array}{|c|c|c|} \hline
\text{Standard} & \text{Trigonometric} & \text{Trigonometric} \\
\text{Form} & \text{Form (deg)} & \text{Form (rad)} \\ \hline
-8i & 8\ \text{cis}\ 270^\circ & 8\ \text{cis}\ 3\pi/2 \\ \hline
\end{array}$
