Lesson Plan: The 𝑛th Roots of Unity | Nagwa Lesson Plan: The 𝑛th Roots of Unity | Nagwa

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.

Objectives

Students will be able to

  • find the 𝑛th roots of unity and understand the derivation of the formula using de Moivre’s Theorem,
  • plot the 𝑛th roots of unity on an Argand diagram and understand the geometric properties of this diagram,
  • solve problems using the properties of the 𝑛th roots of unity,
  • understand the relationship between 𝑛th and 𝑛th roots of unity where 𝑛 and 𝑛 share a factor,
  • understand the definition of a primitive root of unity.

Prerequisites

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.

Exclusions

Students will not cover

  • 𝑛th roots of an arbitrary complex number.

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