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

traces out
counter-clockwise circular motion along the unit
circle in the complex plane as

increases, while
gives
clockwise circular motion.
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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