Convert the given complex number in polar form: i
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.

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