Roots of Unity 02 coordinate and angle magnitude arithmetic of complex numbers
Channel: Anatomy of Algebra
Date: 2020-10-27

The complex numbers are more reasonable seeming if we draw their picture: a plane of points. Once we do this, we can think about them in terms of x and y coordinates, a real and imaginary part. Then a lot of the intuition we have about adding and coordinate geometry comes into play. Even better though, if we think about points in the plane as having magnitude and angle, we can tie the arithmetic of multiplication to the geometry of magnitudes and angles. This is the key to finding the roots of unity.