Euler_s_Identity_I - positive real number Next | Prev | Up...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Next | Prev | Up | Top | Index | JOS Index | JOS Pubs | JOS Home | Search Euler's Identity Euler's identity (or ``theorem'' or ``formula'') is (Euler's Identity) To ``prove'' this, we will first define what we mean by `` ''. (The right-hand side, , is assumed to be understood.) Since is just a particular real number , we only really have to explain what we mean by imaginary exponents . (We'll also see where comes from in the process.) Imaginary exponents will be obtained as a generalization of real exponents . Therefore, our first task is to define exactly what we mean by , where is any real number, and is any
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: positive real number. Next | Prev | Up | Top | Index | JOS Index | JOS Pubs | JOS Home | Search [How to cite this work] [Order a printed hardcopy] [Comment on this page via email] `` 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 © 2011-04-23 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University Page 1 of 1 Euler's Identity 10/4/2011
View Full Document

Ask a homework question - tutors are online