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The Roots of Unity

The Roots of Unity
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2017-10-17 01:40
VectorComplex NumberTransformation
This example demonstrates the concept of roots of unity. Roots of unity are points on the complex plane whose powers equal 1. Through rotation and vector operations, the properties of roots of unity are visually understood. Commands such as rotation, vector, and complex number are used. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Rotate(C, (360 / β)°, A) → Nroot
  4. Angle(C, A, Nroot) → α_1
  5. ToComplex(Vector[Nroot]) → u
  6. ToPolar(Vector[Nroot]) → v
  7. Vector(NrootPower) → w
  8. ToPolar(w) → z
  9. Angle(C, A, NrootPower) → β_1
  10. ToComplex(w) → a
  11. Ray(A, w) → h
  12. Intersect(c, h) → B,