Roots of Unity: Polar Form (1 of 2)
This video introduces the idea of finding the roots of unity, or, in other words, finding the various roots of the number one.
Specifically, the video examines the equation z^5 = 1 which asks us to determine the 5th roots of the number one. There are 5 solutions since whatever power z is raised to is how many solutions exist. The more obvious solution is z = 1, but every other solution is a complex number.
There are two general strategies for solving this equation. Each side of the equation can be rewritten in either polar or exponential form and the magnitudes and angles can be compared on both sides. This video uses the strategy of rewriting everything in polar form and a later video will examine exponential form using Euler's formula. The exponential form is generally faster.
Khan Academy exercise to practice:
1. Powers of Complex Numbers: https://www.khanacademy.org/math/prec...
EulersAcademy.org