The Open University since 2006
Alternatively you can skip the navigation by pressing 'Enter'.
Frozen Planet: WinterWednesday, 25th May 2016 09:00 - EdenTemperatures plummet to 70 below - and the Poles become unforgiving places Read more: Frozen Planet: Winter
Life - with David Attenborough: BirdsWednesday, 25th May 2016 11:00 - Eden
Frozen Planet: WinterWednesday, 25th May 2016 15:00 - Eden
All in the Mind - Summer 2016: Exams and the mental health of children, a community approach to suicide preventionWednesday, 25th May 2016 15:30 - BBC Radio 4
Old School With The Hairy Bikers: EPISODE 3Available until Sunday, 26th June 2016 20:00With only four weeks left at the Oxford Academy, we look to see how the old and young have learned from each other. Read more: Old School With The Hairy Bikers: EPISODE 3
All in the Mind - Summer 2016: Exams and the mental health of children, a community approach to suicide preventionAvailable until Wednesday, 24th May 2017 00:00
Thinking Allowed 2016: Glasgow gangs - Russian gangsAvailable for over a year
Shakespeare Speaks: Cruel to be kindAvailable until Monday, 20th June 2016 00:00
Life - with David AttenboroughDavid Attenborough explores the vibrant mix of life found on our plant - where it comes from, and... Read more: Life - with David Attenborough
Take the photographic memory testCan you capture scenes just by looking at them? Find out with our photographic memory test. Launch now: Take the photographic memory test
Constitutions in transitionThis free course, Constitutions in transition, explores and compares the development of four... Try: Constitutions in transition now
Introduction to bookkeeping and accountingLearn about the essential numerical skills required for accounting and bookkeeping. This free... Try: Introduction to bookkeeping and accounting 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.