# Powers of Complex Numbers

This environment allows you to explore what happens when you raise a complex number to a power.
Drag the yellow dot to position the complex number Z = a + bi.
Show or hide the complex conjugate of Z, i.e. Z* = a - bi

**Challenge - Why are there spirals? How are the spirals of Z and Z* related? Why? What is the circle and why is it there?**## New Resources

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