# Trigonometry Examples

Reorder and .

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

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

where

Substitute the actual values of and .

Raise to the power of to get .

Raise to the power of to get .

Add and to get .

Rewrite as .

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

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

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

Substitute the values of and .