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