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Complex Powers of the Unit Circle

Complex Powers of the Unit Circle
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2018-02-18 08:36
CircleSequenceComplex Number
This example demonstrates how the complex powers of the unit circle generate complex geometric patterns. It involves core concepts of complex numbers and trigonometry. Using the GeoGebra command Sequence, a series of points representing the positions of different complex powers on the unit circle are constructed. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Sequence((cos(t), sin(t), 0), t, 0, (2 * π), π / 180) → L1
  2. Sequence((cos((n * t)), sin((n * t)), 2), t, 0, (2 * π), π / 180) → L2
  3. Sequence(Segment[L1(w), L2(w)], w, 1, Length[L1]) → L3