Roots of Unity are complex numbers that, when raised to a certain integer power, equal 1. Specifically, the n-th roots of unity are the solutions to the equation z^n = 1 . These roots can be represented on the complex plane as points on the unit circle, evenly spaced around the circle, with each root corresponding to an angle of \frac2\pi kn for k = 0, 1, 2, \ldots, n-1 . The concept of Roots of Unity is important in various fields, including algebra, number theory, and signal processing. They play a crucial role in Fourier transforms and are used in polynomial equations to simplify calculations and understand periodic phenomena.