Complex Number Worksheets

Solutions

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

2Solve:

1 Quotient of a Complex Number

2 Complex Number Exercises

3 Complex Number Exercises

4 Complex Number Radical

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

Complex Number Exercises

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

5 Calculate Complex Number Exercises, and show the result in polar form.

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

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

Complex Number Exercises

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


Complex Number Worksheets

1

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

Complex Number Roots

Complex Number Operations

Complex Number Operations

Complex Number Solution


2

Solve:

1 Complex Number Exercises

Complex Number Solution


2 Complex Number Exercises

Complex Number Operations

Complex Number Solution


3 Complex Number Exercises

Complex Number Operations

Complex Number Solution


4 Complex Number Exercises

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Solution


3

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

Complex Number Exercises

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Solution


4

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

Complex Number Exercises

Complex Number Operations

Complex Number Operations

Complex Number Solution


5

Calculate Complex Number Exercises, and show the result in polar form.

Complex Number Operations

Complex Number Operations

Complex Number Solution


6

Calculate the value of Complex Number Exercises, and represent the cubic root affixes.

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Solution


7

Express a complex number in polar form whose cube is:

Complex Number Exercises

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations


8

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

cos 3α and sin 3α


Binomial theorem

Binomial Theorem

Binomial Theorem


Moivre's formula

Moivre's Formula

Moivre's Formula

Complex Number Solution


9

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

14 + 4i

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Solution


2−2 + 2i

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Solutions


10

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

Roots of the Equation

Complex Number Operations

Complex Number Argument


11

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

cos 5α and sin 5α

Binomial theorem

Binomial Theorem

Binomial Theorem

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Operations

Complex Number Solutions


Moivre's formula

Moivre's Formula

Complex Number Operations

Complex Number Solution