### Introduction

In the first part of this Section we introduce a geometrical interpretation of a complex number. Since a complex number $z=x+iy$ is defined by two real numbers $x$ and $y$ it is natural to consider a plane in which to place a complex number. We shall see that there is a close connection between complex numbers and two-dimensional vectors.

In the second part of this Section we introduce an alternative form, called the polar form, for representing complex numbers. We shall see that the polar form is particularly advantageous when multiplying and dividing complex numbers.

#### Prerequisites

- know what a complex number is
- be able to use trigonometric functions $sin$ , $cos$ and $tan$
- understand what a polynomial is
- possess a knowledge of vectors

#### Learning Outcomes

- represent complex numbers on an Argand diagram
- obtain the polar form of a complex number
- multiply and divide complex numbers in polar form

#### Contents

1 The argand diagram2 The polar form of a complex number

2.1 Multiplication and division using polar coordinates

2.2 Complex numbers and rotations