Notes on the Complex Roots of Unity

The article explains how to find the complex roots of unity—complex numbers that equal 1 when raised to a positive integer power n. While real roots of unity are limited (only 1 for odd-degree roots, and 1 or -1 for even-degree roots), complex roots are far more numerous and can be calculated using polar coordinates with the formula z_k = e^(i2πk/n) for k = 0, 1, ..., n-1. The article demonstrates this method with concrete examples, showing how n-th roots of unity are evenly distributed around the unit circle in the complex plane.