Answer
(a) See the picture.
(b)
$r=\sqrt {2}$
$θ=\frac{3\pi}{4}$
(c)
$z=\sqrt 2(cos\frac{3\pi}{4}+i~sin\frac{3\pi}{4})$
Work Step by Step
(b)
$r=|z|=\sqrt {a^2+b^2}=\sqrt {(-1)^2+1^2}=\sqrt {2}$
$tan~θ=\frac{b}{a}=\frac{1}{-1}=-1$
$θ=\frac{3\pi}{4}$
(c)
$z=r(cos~θ+i~sin~θ)$
$z=\sqrt 2(cos\frac{3\pi}{4}+i~sin\frac{3\pi}{4})$
