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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 unit 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 unit is an adapted extract from the Open University course
This unit 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.
Copyright & revisions
Originally published: Monday, 13th June 2011
Last updated on: Monday, 25th July 2011
- 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.
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