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Lesson: Cube Roots of Unity Mathematics

In this lesson, we will learn how to identify the cubic roots of unity using de Moivre’s theorem.

Lesson Plan

Objectives

Students will be able to

find the cube roots of unity and understand the derivation of the formula using de Moivre’s theorem,
plot the cube roots of unity on an Argand diagram and understand the geometric properties of this diagram,
solve problems using the properties of the cube roots of unity,
understand the definition of the primitive cube 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 forms,
representing a complex number on an Argand diagram.

Exclusions

Students will not cover

roots of unity.

Lesson Video

Lesson Explainer

+9

Sample Question Videos

02:10

Lesson Worksheet

Q1:

If , where is a positive integer and is one of the complex cubic roots of unity, then what is ?

Q2:

Write in its simplest form, where is a primitive cube root of unity.

Q3:

Write in its simplest form, where is a primitive cube root of unity.

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