# Lesson Worksheet: Cube Roots of Unity Mathematics

In this worksheet, we will practice identifying the cubic roots of unity using de Moivre’s theorem.

Q1:

Find all the values of for which .

• A,
• B,
• C,
• D,
• E,

Q2:

Let and be the complex cubic roots of unity.

Evaluate . How does this compare with ?

• A,
• B,
• C,
• D,
• E,

Evaluate . How does this compare with ?

• A,
• B,
• C,
• D,
• E,

Q3:

Evaluate where is a complex cube root of unity.

Q4:

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

• A
• B
• C1

Q5:

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

• A
• B
• C1

Q6:

Evaluate , where is a primitive cube root of unity.

• A1
• B
• C
• D
• E

Q7:

Evaluate where is a complex cube root of unity.

Q8:

Evaluate , where is a nontrivial cubic root of unity.

• A
• B
• C
• D

Q9:

Given that is one of the complex cubic roots of unity, find the complex conjugate of .

• A
• B
• C
• D

Q10:

What is , where is a primitive cube root of unity?

• A49
• B48
• C0
• D57