Question

Convert the following complex number into its polar representation: 3i O A. -3(60597 +isin 37 O COS 2 2 O B. -3(cos+ i sin o) O C. 3(cos+ i sin ) O D. 3c052+isin 8

Answer 1

The correct option is D.

The value of r for the given complex number is calculated below:

$r=\sqrt[]{0^2+3^2}=\sqrt[]{9}=3$

now,

$\tan \theta=\frac{3}{0}=\text{ not defined}$

Since the complex number lies on the positive y-axis.

$\theta=\frac{\pi}{2}$

Therefore, the polar form of the given complex number is

$3(\cos \frac{\pi}{2}+i\sin \frac{\pi}{2})$