Answer
(a) See the graph
(b)
$r=4\sqrt 2$
$θ=\frac{\pi}{4}$
(c)
$z=4\sqrt 2(cos\frac{\pi}{4}+i~sin\frac{\pi}{4})$
Work Step by Step
(b)
$r=|z|=\sqrt {a^2+b^2}=\sqrt {4^2+4^2}=\sqrt {32}=4\sqrt 2$
$tan~θ=\frac{b}{a}=\frac{4}{4}=1$
$θ=\frac{\pi}{4}$
(c)
$z=r(cos~θ+i~sin~θ)$
$z=4\sqrt 2(cos\frac{\pi}{4}+i~sin\frac{\pi}{4})$
