# 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