This environment allows you to explore what happens when you raise a complex number to a power. Drag the black dot to position the complex number Z = a + bi - you can show or hide the complex conjugate of Z, i.e. Z*, the inversion of Z in the unit circle, and the inversion of Z* in the unit circle. Watch an animation by clicking in the lower left hand corner of the window. Challenge - Why are there spirals? How are the spirals of Z and Z* related? Why? How are the spirals of the inversions of Z and Z* related to the spirals of Z and Z*?