Dave's Short Course on

In one section some background in trigonometry is needed as indicated with the symbol. That section goes further into complex numbers and is optional in an introduction.

1.  Quadratic and cubic equations

Solution of quadratics, solution of cubics

2.  The Fundamental Theorem of Algebra

3.  The number i

The Fundamental Theorem of Algebra proved!

II.  Mathematics

4.  The complex plane, addition and subtraction

Notation, arithmetic operations on C, parallelogram rule, addition as translation, negation and subtraction

5.  Absolute value

The unit circle, the triangle inequality

6.  Multiplication

Multiplication done algebraically, multiplying a complex number by a real number, multiplication and absolute value, powers of i, roots of unity, multiplying a complex number by i, a geometric interpretation of multiplication

7.  Angles and polar coordinates

8.  Reciprocals, conjugation, and division

Reciprocals done geometrically, complex conjugates, division

9.  Powers and roots

Powers, roots, more roots of unity

Special symbols used here. Some old web browsers do not display mathematical symbols. The following table shows the mathematical symbols used here. If there are any entries in the first column that appear blank or appear as question marks, then your web browser will not display those symbols, and you will need to use a different web browser to see all the symbols.

© 1999.
David E. Joyce
Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610

Email: djoyce@clarku.edu

These pages are located at http://www.clarku.edu/~djoyce/complex/