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

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.

Q1:

Find all the values of for which .

Q2:

Let and be the complex cubic roots of unity.

Evaluate . How does this compare with ?

Q3:

Evaluate where is a complex cube root of unity.