Powers of a complex number

Author:Bill Zahner

This sketch shows complex number z in blue, as well as z^2, z^3, ... , z^50. Try moving z slowly and notice what happens. Why is this happening? Can you make any pretty designs with this sketch?

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Rolling Circles and Polygons
Building Trapezoids with Set Areas
Perimeter of Rectangle
Building Parallelograms with Set Areas
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Unit 2 pt. 1
parabola
Problem 9 from page 37
Exploring Properties of Parallel Lines #4
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Curve Sketching
Piecewise Functions
Linear Functions
Area
Percentages