Question

Determine the polar form of the complex number 3-2i complex plane and polar formOf complex numbers?

Determine the polar form of the complex number 3-2i Express the angle theta in degrees, where 0<theta<360 and round numeric entries in the answer to two decimal places

Answer 1

Step 1:

The complex number is .

Consider .

Polar form of a complex number is    (1)

Here and .

Where is magnitude of complex number and is defined as and is argument of .

Step 2:

Magnitude of complex number  is .

Here and .

and .

and

cosine function is positive and sine function is negative, which means that lies in fourth quadrant.

Thus , angle satisfies both functions is .

Substitute and in  expression (1).

Solution:

The polar form of the complex number is .