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# Algebra Examples

Step 1

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

Step 2

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

where

Step 3

Substitute the actual values of and .

Step 4

Step 4.1

Raise to the power of .

Step 4.2

Raise to the power of .

Step 4.3

Add and .

Step 4.4

Rewrite as .

Step 4.4.1

Factor out of .

Step 4.4.2

Rewrite as .

Step 4.5

Pull terms out from under the radical.

Step 5

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

Step 6

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

Step 7

Substitute the values of and .

Step 8

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