NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Introduction to Complex Numbers

This chapter provides an introduction to complex numbers, factoring polynomials, the quadratic formula, the complex plane, Euler's formula, and an overview of numerical facilities for complex numbersin Matlab and Mathematica.

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Subsections

• Factoring a Polynomial with Real Roots
• The Quadratic Formula
• Complex Roots
• The Fundamental Theorem of Algebra
• Complex Numbers
  • The Complex Plane
  • More Notation and Terminology
  • Elementary Relationships
  • Euler's Formula
  • De Moivre's Theorem
• Numerical Tools in Matlab
• Numerical Tools in Mathematica

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