Answer
The negative of z is
$-z = r[cos(\theta + \pi) + i\cdot sin(\theta + \pi)]$
Work Step by Step
For $z = r(cos\theta + i\cdot sin\theta)$ or in rectangular form $z = a + bi$,
By comparing, $a = rcos\theta$ and $b = rsin\theta$
The negative of $z$ is
$-z$
= $-(a + bi)$
= $-a - bi$
= $-rcos\theta - i\cdot rsin\theta$
= $r(-cos\theta - i\cdot sin\theta)$
= $r[cos(\theta + \pi) + i\cdot sin(\theta + \pi)]$
