Worksheet: Cube Roots of Unity
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.
- A
- B
- C1
Q4:
Evaluate , where is a primitive cubic root of unity.
- A19,683
- B
- C
- D
- E
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
- B
- C1
- D0
Q8:
Evaluate where is a complex cube root of unity.
- A
- B
- C0
- D
Q9:
What is ?
- A49
- B48
- C0
- 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 .
- A1
- B
- C
- 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 .
- A
- B
- C1
- 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
- B1
- C
- D
Q18:
Evaluate , where is a primitive cubic root of unity.
- A
- B1
- C
- D
- E
Q19:
Evaluate where is a complex cube root of unity.
Q20:
Evaluate , where is a primitive cubic root of unity.
- A
- B
- C
- D1
- E
Q21:
Write in its simplest form.
- A
- B1
- C
Q22:
Write in its simplest form.
- A
- B1
- C
Q23:
Write in its simplest form.
- A
- B1
- C