**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW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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## More Notation and Terminology

It’s already been mentioned that the rectilinear coordinates of a complex number in the complex plane are called the

real partandimaginary part, respectively.We also have special notation and various names for the radius and angle of a complex number expressed in polar coordinates :

The

complex conjugateof is denoted and is defined by

where, of course, . Sometimes you’ll see the notation in place of , but we won’t use that here.In general, you can always obtain the complex conjugate of any expression by simply replacing with . In the complex plane, this is a

vertical flipabout the real axis; in other words, complex conjugation replaces each point in the complex plane by itsmirror imageon the other side of the axis.