Question

Convert the given complex number in polar form: $i$

Answer 1

$z=i$
Let $r\cos \theta =0$ and $r\sin \theta =1$
On squaring and adding, we obtain
$r^2{\cos }^2\theta +r^2{\sin }^2\theta =0^2+1^2$
$\Rightarrow r^2({\cos }^2\theta +{\sin }^2\theta )=1$
$\Rightarrow r^2=1$
$\Rightarrow r=\sqrt{1}=1$ (Since, $r>0$)
$\therefore \cos \theta =0$ and $\sin \theta =1$
$\therefore \theta =\frac{\pi }{2}$
So, the polar form is
$\therefore i=r\cos \theta +ir\sin \theta =\cos \frac{\pi }{2}+i\sin \frac{\pi }{2}$