traces out counter-clockwise circular motion along the unit circle in the complex plane, while
is clockwise circular motion.
We call a complex sinusoid of the form , where , apositive-frequency sinusoid. Similarly, we 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.
REMARK: Add figure: circular motion (animation for web version)