An introduction to complex numbers

1.1 Workbook contents

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. Section 4.2 of the unit requires you to listen to some audio files. You'll find these on the next page of this unit.

Click on 'View document' to open the workbook (PDF, 4 MB).

Click on 'View document' to open the answer book (PDF, 4.2 MB).

• Introduction

  • Study Guide

• 1 Introducing complex numbers

  • 1.1 What is a complex number?

  • 1.2 Arithmetic in

  • 1.3 Identities with complex numbers

• 2 The complex plane

  • 2.1 Cartesian coordinates

  • 2.2 Polar form

  • 2.3 The geometric interpretation of multiplication and division

  • 2.4 de Moivre's Theorem

• 3 Solving equations with complex numbers

  • 3.1 Calculating nth roots

  • 3.2 Solutions of polynomial equations

• 4 Sets of complex numbers

  • 4.1 Inequalities

  • 4.2 Sketching subsets of the complex plane (audio tape)

• 5 Proving inequalities

  • 5.1 Rules for rearranging inequalities

  • 5.2 The triangle inequality

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