Lesson Worksheet: Cube Roots of Unity Mathematics

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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 .

Q2:

Let and be the complex cubic roots of unity.

Evaluate . How does this compare with ?

Q3:

Evaluate where is a complex cube root of unity.

Q4:

Write in its simplest form, where is a primitive cube root of unity.

Q5:

Write in its simplest form, where is a primitive cube root of unity.

Q6:

Evaluate , where is a primitive cube root of unity.

Q7:

Evaluate where is a complex cube root of unity.

Q8:

Evaluate , where is a nontrivial cubic root of unity.

Q9:

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

Q10:

What is , where is a primitive cube root of unity?

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