Answer
$\color{blue}{\sqrt{2}\ \text{cis}\ 135^\circ, \sqrt{2}\ \text{cis}\ 3\pi/4}$
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: $\quad\tan\theta = y/x = 1/(-1) = -1 \implies \theta = 135^\circ \equiv 3\pi/4$ (smallest positive real angle $\theta$ from $+x$-axis to graph of $z$)
$\begin{array}{|c|c|c|} \hline
\text{Standard} & \text{Trigonometric (deg)} & \text{Trigonometric (rad)} \\
\text{Form} & \text{Form} & \text{Form} \\ \hline
-1+i & \sqrt{2}\ \text{cis}\ 135^\circ & \sqrt{2}\ \text{cis}\ 3\pi/4 \\ \hline
\end{array}$
