Question:
Convert the given complex number in polar form: $i$
Solution:
$i$
Let $r \cos \theta=0$ and $r \sin \theta=1$
On squaring and adding, we obtain
$r^{2} \cos ^{2} \theta+r^{2} \sin ^{2} \theta=0^{2}+1^{2}$
$\Rightarrow r^{2}\left(\cos ^{2} \theta+\sin ^{2} \theta\right)=1$
$\Rightarrow r^{2}=1$
$\Rightarrow r=\sqrt{1}=1$ [Conventionally, $r>0$ ]
$\therefore \cos \theta=0$ and $\sin \theta=1$
$\therefore \theta=\frac{\pi}{2}$
$\therefore i=r \cos \theta+i r \sin \theta=\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}$
This is the required polar form.