Answer
$8(\displaystyle \cos\frac{\pi}{2}+i\sin\frac{\pi}{2})$
Work Step by Step
We are given:
$z=8i=0+8i$
To find $r$ of a complex number $a+bi$, we use: $\sqrt{a^2+b^2}$:
$r=\sqrt{0^{2}+8^{2}}=8$
To find $\theta$, we use $\tan{\theta}=\frac{b}{a}$:
$\displaystyle \tan\theta=\frac{8}{0}$=undefined (or +$\infty$)
And since $z$ is located at (0,8) (y-axis), we have:
$\displaystyle \theta=\frac{\pi}{2}$
To put the number in polar form, we use $r(\cos{\theta}+i\sin{\theta})$:
$8(\displaystyle \cos\frac{\pi}{2}+i\sin\frac{\pi}{2})$
