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 .

Raise to the power of .

Add and .

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 fourth quadrant, the value of the angle is .

Substitute the values of and .

Replace the right side of the equation with the trigonometric form.

Find All Complex Number Solutions z=3-4i