Powers of Complex Numbers
- Author:
- Judah L Schwartz
- Topic:
- Numbers
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*?