# Worksheet: The nth Roots of Unity

In this worksheet, we will practice using de Moivre's theorem to find the nth roots of unity and exploring their properties.

**Q1: **

Which of the following is a general form for the roots in exponential form?

- A
- B
- C
- D
- E

**Q2: **

Let be an root of unity. When can we define as a primitive root of unity?

- AWhen it is an root of unity for some
- BWhen it is an root of unity, where is a prime number
- COnly when is a prime number
- DWhen it is not an root of unity for some
- EOnly when is an even number

**Q3: **

If is a primitive root of unity, which of the following expressions is equivalent to ?

- A
- B
- C
- D1
- E

**Q4: **

Which of the following is one of the roots of unity in Cartesian form?

- A
- B
- C
- D
- E

**Q5: **

Let be one of the quintic roots of unity. Which of the following is an equivalent expression to ?

- A
- B
- C
- D
- E

**Q6: **

Let be an root of unity and be a positive integer. Which of the following is **not** an equivalent expression for ?

- A
- B
- C
- D
- E

**Q7: **

Let be an root of unity, where is even. Which of the following expressions is equivalent to ?

- A
- B
- C
- D
- E

**Q8: **

How many of the 8th roots of unity are also 12th roots of unity?

**Q9: **

What is the general form for the 10th roots of unity in polar form?

- A
- B
- C
- D
- E

Using the general form for 10th roots of unity, identify the 10th root of unity for the case where .

- A
- B
- C
- D
- E

**Q10: **

Which of the following is **not** one of the cube roots of unity?

- A
- B
- C
- D
- E1