MathPlotAI Logo MathPlotAI

nth Roots of Unity

nth Roots of Unity
Loading the math board and drawing, please wait…
2018-12-08 15:01
CircleComplex NumberGeometric Construction
This example demonstrates the geometric representation of nth roots of unity. Key mathematical concepts include complex numbers and the unit circle. Using GeoGebra commands such as Intersect, Circle, and Sequence, the nth roots of unity can be constructed. Suitable for high school mathematics education, particularly in the teaching of complex numbers and trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c
  3. Vector(O, Z) → ZVector
  4. Circle(O, Z) → ZCircle
  5. Sequence((Z^(1 / n) * ℯ^((((ί * 2) * π) * k / n))), k, 0, n - 1) → Roots
  6. Circle(O, abs(ZVector)^(1 / n)) → WCircle
  7. Sequence(Text["W_{" + ((k * "}")), Element[Roots, k], n > 0, n > 0], k, 1, n) → RootsLabels
  8. Sequence(Vector[O, Element[Roots, k]], k, 1, n) → RootsVectors
  9. Point(WCircle) → W
  10. Sequence(Circle[O, abs(W^(k))], k, 2, n - 1) → WCircles
  11. Sequence(Vector[O, W^(k)], k, 1, n) → WVectors
  12. Vector(O, (1, 0)) → u
  13. Sequence(Text["W^{" + (k) + "}", W^(k), n > 0, n > 0], k, 2, n) → WLabels
  14. Text("W", W) → textW
  15. Sequence(Text["W^{" + (k) + "}, \angle" + (Angle[u, Vector[W^(k)]]), W^(k), n > 0, n > 0], k, 2, n) → WLabelsAngles
  16. Text("W, ∠" + (Angle[u, Vector[W]]), W) → textWAngles
  17. Text("Z, ∠" + (Angle[u, Vector[Z]]), Z) → textZAngles
  18. Text("Z", Z) → textZ
  19. Sequence(Text["W_{" + ((k * "}, \angle")) + (Angle[u, Vector[Element[Roots, k]]]), Element[Roots, k], n > 0, n > 0], k, 1, n) → RootsLabelsAngles