Unit Circle

The unit circle is a circle of radius 1, typically centered at (0, 0) in the coordinate plane when used in a coordinate geometry context. It can be used to demonstrate trigonometric functions such as sin, cos, and tan, but it is most commonly used to visualize the complex numbers. This is done by setting the y-axis as units of i, where i is the square root of -1. The unit circle in the complex plane represents the set of all complex numbers with a magnitude of 1. Because of this, any number on this unit circle raised to any power will still yield a number on the unit circle, but possibly at a different rotation. In fact, multiplying numbers on the circle is equivalent to simply adding their angles respective to the positive x-axis.