Answer
$z=5(\displaystyle \cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})$
Work Step by Step
See p. 604,
A complex number $z=a+bi$ has the polar (or trigonometric) form
$z=r(\cos\theta+i\sin\theta)$
where $r=|z|=\sqrt{a^{2}+b^{2}}$ and $\tan\theta=b/a$.
The number $r$ is the modulus of $z$, and $\theta$ is an argument of $z$.
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$z=0-5i$
$r=|z|=\sqrt{(0)^{2}+(5)^{2}}=5$
$\tan\theta$ is undefined,
$\displaystyle \tan\frac{\pi}{2}$ is undefined.
By symmetry (on the unit circle),
$\theta$ can also be $\displaystyle \frac{3\pi}{2}$ (negative imaginary axis).
$z=0-5i$
lies on the negative imaginary axis, so we select the appropriate argument:
$z=5(\displaystyle \cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})$
