Dave's Short Course on

IntroductionThis is an introduction to complex numbers. It includes the mathematics and alittle bit of history as well. It is intended for a general audience. The necessarybackground in a familiarity with ordinary real numbers (all positive andnegative numbers and zero) and algebra.In one section some background in trigonometry is needed as indicated with the

symbol. That section goes further into complex numbers and is optionalin an introduction.

Table of contentsI. History

1. Quadratic and cubic equationsSolution of quadratics, solution of cubics

2. The Fundamental Theorem of Algebra3. The number i

The Fundamental Theorem ofAlgebra proved!

II. Mathematics4. The complex plane, addition andsubtraction

Notation, arithmetic operationson C, parallelogram rule,addition as translation, negationand subtraction

Complex numbers http://www.clarku.edu/~djoyce/complex/

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5. Absolute valueThe unit circle, the triangleinequality

6. MultiplicationMultiplication done algebraically, multiplying a complex number by areal number, multiplication and absolute value, powers of i, roots ofunity, multiplying a complex number by i, a geometric interpretationof multiplication

7. Angles and polar coordinates8. Reciprocals, conjugation, and division

Reciprocals done geometrically, complex conjugates, division9. Powers and roots

Powers, roots, more roots of unity

Select topic

Daves Short Course on Complex Numbers islocatedat http://www.clarku.edu/~djoyce/complex/

1999, 2013David E. Joyce

Department of Mathematics and ComputerScience

Clark UniversityWorcester, MA 01610

Complex numbers http://www.clarku.edu/~djoyce/complex/

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