复数根的几何展示：利用De Moivre定理可视化n次根

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → O
2. Sequence(Z^(1 / n) * exp(i * 2 * 3.141592653589793 * k / n), k, 0, n - 1) → Roots
3. Circle(O, Z) → ZCircle
4. Vector(O, Z) → ZVector
5. Circle(O, abs(ZVector)^(1 / n)) → WCircle
6. Point(WCircle) → W
7. Sequence(Text["W^{" + (k) + "}", W^(k), n > 0, n > 0], k, 2, n) → WLabels
8. Sequence(Vector[O, W^(k)], k, 1, n) → WVectors
9. Sequence(Text["W_{" + (k) + "}", Element[Roots, k], n > 0, n > 0], k, 1, n) → RootsLabels
10. Sequence(Vector[O, Element[Roots, k]], k, 1, n) → RootsVectors
11. Sequence(Circle[O, abs(W^(k))], k, 2, n - 1) → WCircles