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.