# Trigonometry Examples

Step 1

Reorder and .

Step 2

This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.

Step 3

The modulus of a complex number is the distance from the origin on the complex plane.

where

Step 4

Substitute the actual values of and .

Step 5

Step 5.1

Raise to the power of .

Step 5.2

Raise to the power of .

Step 5.3

Add and .

Step 5.4

Rewrite as .

Step 5.5

Pull terms out from under the radical, assuming positive real numbers.

Step 6

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

Step 7

Since inverse tangent of produces an angle in the first quadrant, the value of the angle is .

Step 8

Substitute the values of and .