Lesson Plan: The 𝑛th Roots of Unity Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use de Moivre’s theorem to find the 𝑛th roots of unity and explore their properties.
Students will be able to
- find the roots of unity and understand the derivation of the formula using de Moivre’s Theorem,
- plot the roots of unity on an Argand diagram and understand the geometric properties of this diagram,
- solve problems using the properties of the roots of unity,
- understand the relationship between and roots of unity where and share a factor,
- understand the definition of a primitive root of unity.
Students should already be familiar with
- de Moivre’s theorem,
- different forms of complex numbers including Cartesian (algebraic , rectangular), polar (trigonometric), and exponential,
- representing a complex number on an Argand diagram.
Students will not cover
- roots of an arbitrary complex number.