Deriving and Graphing Complex Roots of Unity
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Video Lecture 22 of 26
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### Lecture Description

Complex Analysis, Video #22 (Complex Arithmetic, Part 22).

When you find roots of complex numbers, you get more than one answer (roots are "multi-valued functions"). We're focusing at the moment on finding roots of "unity" (one). The notation 1^(1/3), for instance, represents all possible cube roots of one. We get more than one answer because of the multiplicity of polar representations of complex numbers. Using the polar form of a possible root, we can easily derive the roots. In this video, the main example is to find the 12th roots of unity, 1^(1/12). Find the 12 distinct roots in polar form and then use ListPlot and Table to plot the roots. Also use Graphics and Line along with Table to graph line segments from the origin to the roots. Notice that they are all 30 degrees apart, which makes sense because 360/12 = 30. Also note that we could connect successive roots and get a regular 12-gon (dodecagon).

### Course Description

This is a mini crash course providing all you need to know to understand complex numbers, and study Complex Analysis. Mathematica is used to help visualize the complex plane.