The Fundamental Theorem of Algebra

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. The Fundamental Theorem of Algebra

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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The Fundamental Theorem of Algebra

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


we can always rewrite it as
\


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

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