Question

Represent the complex number graphically, and find the trigonometric form of the number.

- 2(1 + √3 i)

Answer 1

Step 1:

Graph of the complex number .

Step 2:

The complex number

Consider

Compare the complex number to .

The absolute value of the complex number is .

And the reference angle is given by

and is lies in the third quadrant

Reference angle

The trigonometric form of the complex number is

Substitute corresponding values in the above expression.

Solution:

Graph of the complex number .:

The trigonometric form of the complex number .