Answer
$\color{blue}{\sqrt{2}\ \text{cis}\ 225^\circ, \sqrt{2}\ \text{cis}\ 5\pi/4}$
Work Step by Step
$z=-1-i = x+iy \implies x=-1, y=-1$
$\Huge\cdot$ modulus: $\quad r = \sqrt{x^2+y^2} = \sqrt{(-1)^2+(-1)^2}=\sqrt{2}$
$\Huge\cdot$ argument: $\quad \tan\theta = y/x=(-1)/(-1)=1 \implies \theta = 225^\circ \equiv 5\pi/4$ (smallest positive real angle $\theta$ from $+x$-axis to graph of $z$)
$\begin{array}{|c|c|c|} \hline
\text{Standard} & \text{Trigonometric} & \text{Trigonometric} \\
\text{Form} & \text{Form (deg)} & \text{Form (rad)} \\ \hline
-1-i & \sqrt{2}\ \text{cis}\ 225^\circ & \sqrt{2}\ \text{cis}\ 5\pi/4 \\ \hline
\end{array}$