Answer
The conjugate of z is
$\bar{z}$ = $r(cos\theta - i\cdot sin\theta)$ or $r[cos(360^\circ - \theta) + i\cdot sin(360^\circ - \theta)]$
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 $b = rsin\theta$
As the conjugate of $z$ is $\bar{z} = a - bi$,
$\bar{z}$
= $a - bi$
= $rcos\theta - i\cdot rsin\theta$
= $r(cos\theta - i\cdot sin\theta)$