Answer
a. $4\sqrt 2(\cos135^{\circ}+i\sin135^{\circ})$
Work Step by Step
Trigonometric form of $z=x+iy$ is $r(\cos \theta+ i\sin \theta)$
where $r=|z| = \sqrt {x^{2}+y^{2}}=\sqrt {(-4)^{2}+4^{2}}=$
$\sqrt {32}=4\sqrt 2$
and $\theta=\tan^{-1}(\frac{y}{x}), -180^{\circ}$
