# Worksheet: Cube Roots of Unity

Q1:

What is ?

• A
• B1
• C
• D0

Q2:

What is ?

Q3:

What is ?

• A
• B
• C
• D0

Q4:

If , where and are real numbers, then what is .

• A
• B
• C
• D

Q5:

Evaluate .

Q6:

Evaluate .

Q7:

Evaluate .

• A
• B
• C1
• D
• E

Q8:

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

• A
• B
• C
• D

Q9:

Evaluate .

• A
• B
• C
• D1
• E

Q10:

Evaluate .

• A1
• B
• C
• D
• E

Q11:

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

• A
• B
• C1
• D

Q12:

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

Q13:

What is the smallest positive integer value of for which ?

Q14:

Write in its simplest form.

• A1
• B
• C

Q15:

Write in its simplest form.

• A
• B1
• C

Q16:

Write in its simplest form.

• A
• B
• C1

Q17:

Write in its simplest form.

• A
• B1
• C

Q18:

Write in its simplest form.

• A
• B1
• C

Q19:

Write in its simplest form.

• A
• B
• C1

Q20:

Write in its simplest form.

• A1
• B
• C

Q21:

Evaluate .

• A
• B
• C
• D
• E

Q22:

Evaluate .

• A1
• B
• C
• D
• E

Q23:

Evaluate .

• A
• B
• C
• D
• E 19β683

Q24:

Evaluate .

• A
• B
• C
• D
• E27

Q25:

What is ?

• A0
• B48
• C49
• D57