**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW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

**<<
Previous page TOC INDEX Next
page >>**

## The Fundamental Theorem of Algebra

This is a very powerful algebraic tool. It says that given any polynomial

we canalwaysrewrite it as

where the points are the polynomial roots, and they may be real or complex.