Answer
(a) See the graph.
(b)
$r=\sqrt {34}$
$θ=tan^{-1}\frac{3}{5}$
(c)
$z=\sqrt {34}[cos(tan^{-1}\frac{3}{5})+i~sin(tan^{-1}\frac{3}{5})]$
Work Step by Step
(b)
$r=|z|=\sqrt {a^2+b^2}=\sqrt {5^2+3^2}=\sqrt {34}$
$tan~θ=\frac{b}{a}=\frac{3}{5}$
$θ=tan^{-1}\frac{3}{5}$
(c)
$z=r(cos~θ+i~sin~θ)$
$z=\sqrt {34}[cos(tan^{-1}\frac{3}{5})+i~sin(tan^{-1}\frac{3}{5})]$
