This illustrates complex power functions acting on the unit circle. The domain circle is on the bottom, and the range circle is on the top. Each segment joins z on the domain circle to z[sup]n[/sup] on the range circle. The wrapping nature of the power functions becomes apparent as n varies from 1 to 10.

[size=85]"Complex Power Plot" from the Wolfram Demonstrations Project[br] http://demonstrations.wolfram.com/ComplexPowerPlot/[/size]