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复数的N次根 by moebiuscurve

复数的N次根 by moebiuscurve
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2017-04-06 10:24
向量数列复数
本范例演示复数的N次根。核心数学概念包括复数、根的概念以及复数的几何表示。通过使用GeoGebra命令如Intersect、Vector、Circle、Sequence等，可以动态展示复数的N次根。适合高中数学教学和学习。

GeoGebra 命令及参数

  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