An introduction to complex numbers
An introduction to complex numbers

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

An introduction to complex numbers

1 An introduction to complex numbers

1.1 Workbook contents

The main teaching text of this course 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 course requires you to listen to some audio files. You'll find these on the next page of this course.

Click on the link below to open the workbook (PDF, 4 MB).

Workbook [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

Click on the link below to open the answer book (PDF, 4.2 MB).

Answers

  • 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

M337_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371