### Introduction

This module introduces you to STEP 3 questions involving Complex Numbers.

Each STEP 3 module consists of 4 STEP questions, some topic notes and useful formulae, a "hints" sheet and a "solutions" booklet.

STEP questions are challenging, so don't worry if you get stuck. These STEP 3 modules assume that you have already begun to develop your problem-solving skills and approach to STEP questions by working on the Foundation modules and the STEP 2 modules.

### About this assignment

Complex numbers are very geometrical in nature, appearing as they do on an "Argand plane". There are various different ways of representing complex numbers which are useful in different situations.

Probably the most important thing to remember about complex numbers is the identity ${\rm e}^{i \theta} \equiv \cos \theta + i \sin \theta$. Taking $\theta = \pi$ gives the famous result ${\rm e}^{i \pi}+1=0$.

You can find out more about Complex Numbers in this NRICH Advanced Problem Solving module.

You might like to look at questions 1/2 and 9/10 from the Mixed Pure STEP III questions for some more complex number practice.

### Hints, support and self evaluation

The **“Hints"** file gives suggestions and some starting points on how you can tackle the questions. The **"Solutions"** file leads you through one possible solution, but some steps will be missing and you will still need to work through the question yourself.