Complex Powers of the Unit Circle
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 zn on the range circle. The wrapping nature of the power functions becomes apparent as n varies from 1 to 10.
Credit:
"Complex Power Plot" from the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ComplexPowerPlot/