The Open University since 2006
Alternatively you can skip the navigation by pressing 'Enter'.
Thinking Allowed 2016: A special programme on Pierre BourdieuMonday, 27th June 2016 00:15 - BBC Radio 4This special episode of Thinking Allowed explores the ideas of French socialist Pierre Bourdieu. Read more: Thinking Allowed 2016: A special programme on Pierre Bourdieu
Genius of the Modern World: NietzscheAvailable until Friday, 29th July 2016 00:00Bettany Hughes takes us on an exploration of Friedrich Nietzsche's life and works. Read more: Genius of the Modern World: Nietzsche
The Big C & Me: Episode 2Available until Sunday, 24th July 2016 02:05
The Big C & Me: Episode 3Available until Friday, 22nd July 2016 23:55
Thinking Allowed 2016: A special programme on Pierre BourdieuAvailable for over a year
The UK votes out; the EU shrinks; the world reactsReaction from academics around the planet as UK voters elect to leave the E Read more: The UK votes out; the EU shrinks; the world reacts
Genius of the Modern WorldIn this three-part OU/BBC co-production for BBC Four, Bettany Hughes explores the life and works... Watch now: Genius of the Modern World
Grammar mattersGrammar matters because, combined with vocabulary choice, it is our main way of making meaning.... Try: Grammar matters now
Succeed with maths – Part 1If you feel that maths is a mystery that you want to unravel then this free course is for you. It... Try: Succeed with maths – Part 1 now
In this free course, An introduction to complex numbers, you will learn how complex numbers are defined, examine their geometric representation and then move on to looking at the methods for finding the nth roots of complex numbers and the solutions to simple polynominal equations.
After studying this course, you should be able to:
- perform basic algebraic manipulation with complex numbers
- understand the geometric interpretation of complex numbers
- know methods of finding the nth roots of complex numbers and the solutions of simple polynomial equations.
Study this free course
Enrol to access the full course, get recognition for the skills you learn, track your progress and on completion gain a statement of participation to demonstrate your learning to others. Make your learning visible!
An introduction to complex numbers
This course is devoted solely to complex numbers.
In Section 1, we define complex numbers and show you how to manipulate them, stressing the similarities with the manipulation of real numbers.
Section 2 is devoted to the geometric representation of complex numbers. You will find that this is very useful in understanding the arithmetic properties introduced in Section 1.
In Section 3 we discuss methods of finding nth roots of complex numbers and the solutions of simple polynomial equations.
The final two sections deal with inequalities between real-valued expressions involving complex numbers. First we use inequalities in Section 4 to describe various subsets of the complex plane. Then we show, in Section 5, how to prove such inequalities. In particular, we introduce the Triangle Inequality, which can be used to obtain an estimate for the size of a given complex expression.
This OpenLearn course is an adapted extract from the Open University course
Copyright & revisions
Originally published: Monday, 13th June 2011
Last updated on: Tuesday, 15th March 2016
- Creative-Commons: The Open University is proud to release this free course under a Creative Commons licence. However, any third-party materials featured within it are used with permission and are not ours to give away. These materials are not subject to the Creative Commons licence. See terms and conditions. Full details can be found in the Acknowledgements and our FAQs section.
- This site has Copy Reuse Tracking enabled - see our FAQs for more information.
If you enjoyed this, why not follow a feed to find out when we have new things like it? Choose an RSS feed from the list below. (Don't know what to do with RSS feeds?)
Remember, you can also make your own, personal feed by combining tags from around OpenLearn.
All our alternative formats are free for you to download, for more information about the different formats we offer please see our FAQs. The most frequently used are Word (for accessibility), PDF (for print) and ePub and Kindle to download to eReaders*.
- Word (966 KB)
- PDF (2 MB)
- ePub 3.0 (5.9 MB)
- ePub 2.0 (785 KB)
- Kindle (216 KB)
- RSS (169 KB)
- HTML (5.7 MB)
- SCORM (5.7 MB)
- OUXML Package (11 KB)
- OUXML File (36 KB)
- IMS Common cartridge
*Please note you will need an ePub and Mobi reader for these formats.