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

**Q1: **

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

**Q3: **

Write in its simplest form.

- A1
- B
- C

**Q4: **

Evaluate , where is a primitive cubic root of unity.

- A
- B
- C
- D
- E 19,683

**Q5: **

Evaluate , where is a primitive cubic root of unity.

- A
- B
- C
- D1
- E

**Q6: **

Evaluate where is a complex cube root of unity.

**Q7: **

Evaluate where is a complex cube root of unity.

- A
- B1
- C
- D0

**Q8: **

Evaluate where is a complex cube root of unity.

- A
- B
- C
- D0

**Q9: **

What is ?

- A0
- B48
- C49
- D57

**Q10: **

Evaluate where is a complex cube root of unity.

**Q11: **

If , where and are real numbers and is a complex cube root of unity, then what is ?

- A
- B
- C
- D

**Q12: **

Evaluate .

- A
- B
- C1
- D
- E

**Q13: **

What is the smallest positive integer value of for which where is a complex cube root of unity?

**Q14: **

Evaluate , where is a complex cube root of unity.

- A
- B
- C
- D
- E

**Q15: **

Evaluate .

- A1
- B
- C
- D
- E

**Q16: **

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

- A
- B
- C
- D

**Q17: **

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

- A
- B
- C1
- D

**Q18: **

Evaluate , where is a primitive cubic root of unity.

- A
- B
- C
- D
- E1

**Q19: **

Evaluate where is a complex cube root of unity.

**Q20: **

Evaluate , where is a primitive cubic root of unity.

- A1
- B
- C
- D
- E

**Q21: **

Write in its simplest form.

- A
- B1
- C

**Q22: **

Write in its simplest form.

- A
- B
- C1

**Q23: **

Write in its simplest form.

- A
- B1
- C