Since the modulus of the complex sinusoid is constant, it must lie on a
*circle* in the complex plane. For example,

traces out

gives

We may call a complex sinusoid
a
*positive-frequency sinusoid* when
. Similarly, we
may define a complex sinusoid of the form
, with
, to be a
*negative-frequency sinusoid*. Note that a positive- or
negative-frequency sinusoid is necessarily complex.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University