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
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