Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ - Original copyright The Open University
<p>This OpenLearn course is an adapted extract from the Open University course <span class="oucontent-linkwithtip"><a class="oucontent-hyperlink" href="http://www3.open.ac.uk/study/undergraduate/course/m337.htm?LKCAMPAIGN=ebook_&MEDIA=ou">M337 <i>Complex analysis</i></a></span></p><p>This course is devoted solely to complex numbers.</p><p>In Section 1, we define complex numbers and show you how to manipulate them, stressing the similarities with the manipulation of real numbers.</p><p>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.</p><p>In Section 3 we discuss methods of finding <i>n</i>th roots of complex numbers and the solutions of simple polynomial equations.</p><p>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 <i>prove</i> 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.</p>
<p>This course is devoted solely to complex numbers.</p><p>In Section 1, we define complex numbers and show you how to manipulate them, stressing the similarities with the manipulation of real numbers.</p><p>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.</p><p>In Section 3 we discuss methods of finding <i>n</i>th roots of complex numbers and the solutions of simple polynomial equations.</p><p>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 <i>prove</i> 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.</p><p>This OpenLearn course is an adapted extract from the Open University course <span class="oucontent-linkwithtip"><a class="oucontent-hyperlink" href="http://www3.open.ac.uk/study/undergraduate/course/m337.htm?LKCAMPAIGN=ebook_&MEDIA=ou">M337 <i>Complex analysis</i></a></span></p>
<p>This unit is an adapted extract from the Open University course <span class="oucontent-linkwithtip"><a class="oucontent-hyperlink" href="http://www3.open.ac.uk/study/undergraduate/course/m337.htm"><i>Complex analysis</i>
(M337)</a></span></p><p>This unit is devoted solely to complex numbers.</p><p>In Section 1, we define complex numbers and show you how to manipulate them, stressing the similarities with the manipulation of real numbers.</p><p>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.</p><p>In Section 3 we discuss methods of finding <i>n</i>th roots of complex numbers and the solutions of simple polynomial equations.</p><p>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 <i>prove</i> 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.</p>
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.<link rel="canonical" href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/introduction-complex-numbers/content-section-0" /> First published on Mon, 13 Jun 2011 as <a href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/introduction-complex-numbers/content-section-0">An introduction to complex numbers</a>. To find out more visit The Open University's <a href="http://www.open.edu/openlearn/ole-home-page">Openlearn</a> website. Creative-Commons 2011
This unit looks at complex numbers. You will learn how they 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.<link rel="canonical" href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/introduction-complex-numbers/content-section-0" /> First published on Mon, 13 Jun 2011 as <a href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/introduction-complex-numbers/content-section-0">An introduction to complex numbers</a>. To find out more visit The Open University's <a href="http://www.open.edu/openlearn/ole-home-page">Openlearn</a> website. Creative-Commons 2011