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Nth Roots of a Complex Number by moebiuscurve

Nth Roots of a Complex Number by moebiuscurve
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2017-04-06 10:24
VectorSequenceComplex Number
This example demonstrates the Nth roots of a complex number. Key mathematical concepts include complex numbers, roots, and the geometric representation of complex numbers. Using GeoGebra commands such as Intersect, Vector, Circle, and Sequence, the example dynamically shows the Nth roots of a complex number. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

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