# Complex Number Worksheets

### Solutions

1 Calculate all the roots of the equation: x6 + 1 = 0.

2Solve:

1

2

3

4

3 Solve the following root, expressing the results in polar form.

4 Write a quadratic equation which has the solutions 1 + 2i and its conjugate.

5 Calculate , and show the result in polar form.

6Calculate the value of , and represent the cubic root affixes.

7 Express a complex number in polar form whose cube is:

8 Express the following as a function of cos α and sin α:

cos 3α and sin 3α

9 Determine the conjugates and opposites of the following terms in both polar and trigonometrical form:

14 + 4i

2−2 + 2i

10 Calculate all the roots of the equation: x5 + 32 = 0

11 Express the following as a function of cos α and sin α:

cos 5α and sin 5α

## 1

Calculate all the roots of the equation: x6 + 1 = 0.

Solve:

1

2

3

4

## 3

Solve the following root, expressing the results in polar form.

## 4

Write a quadratic equation which has the solutions 1 + 2i and its conjugate.

## 5

Calculate , and show the result in polar form.

## 6

Calculate the value of , and represent the cubic root affixes.

## 7

Express a complex number in polar form whose cube is:

## 8

Express the following as a function of cos α and sin α:

cos 3α and sin 3α

Binomial theorem

Moivre's formula

## 9

Determine the conjugates and opposites of the following terms in both polar and trigonometrical form:

14 + 4i

2−2 + 2i

## 10

Calculate all the roots of the equation: x5 + 32 = 0

## 11

Express the following as a function of cos α and sin α:

cos 5α and sin 5α

Binomial theorem

Moivre's formula