Question:
Write –9 in polar form.
Solution:
We have, z = –9
Let $-9=r \cos \theta$ and $0=r \sin \theta$
By squaring and adding, we get
$(-9)^{2}+(0)^{2}=(r \cos \theta)^{2}+(r \sin \theta)^{2}$
$\Rightarrow 81=r^{2}\left(\cos ^{2} \theta+\sin ^{2} \theta\right)$
$\Rightarrow 81=r^{2}$
$\Rightarrow r=9$
$\therefore \cos \theta=-1$ and $\sin \theta=0$
$\Rightarrow \theta=\pi$
Thus, the required polar form is $9(\cos \pi+i \sin \pi)$