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复数乘法几何解释

复数乘法几何解释
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2014-01-07 12:44
向量复数变换
所属专题 Complex Numbers as Vectors
本范例通过几何方式展示了复数乘法的原理。它涉及复数的向量表示和旋转变换。通过构造向量、旋转、交点等对象，直观地展示了复数乘法的效果。适合初中及以上学生学习复数几何意义。

GeoGebra 命令及参数

  1. Vector(O, P) → z_1
  2. Vector(O, Q) → z_2
  3. Segment(P, A) → a
  4. Segment(A, O) → b
  5. Angle(A, O, P) → α
  6. Rotate(Q, α, O) → Q'
  7. Angle(Q', O, Q) → β_1
  8. Angle(O, A, P) → β
  9. Rotate(O, (-β), Q) → O'
  10. Angle(O', Q, O) → γ
  11. Ray(Q, O') → c
  12. Ray(O, Q') → d
  13. Intersect(d, c) → R
  14. Segment(Q, R) → e
  15. Segment(R, O) → f
  16. Circle(O, 0.3) → g
  17. Midpoint(R, Q) → B
  18. Segment(O, B) → h
  19. Intersect(g, h) → C,
  20. Rotate(Q, (-α), O) → Q'_1
  21. Rotate(O, (-β), Q) → O'_1
  22. Line(O, Q'_1) → i
  23. Rotate(O, β, Q) → O'_2
  24. Line(Q, O'_2) → j
  25. Intersect(j, i) → D
  26. Segment(Q, D) → k
  27. Segment(D, O) → l
  28. Angle(O, Q, D) → δ
  29. Angle(D, O, Q) → ε
  30. Midpoint(Q, D) → E
  31. Segment(O, E) → m
  32. Intersect(g, m) → F,
  33. Circle(Q, 0.3) → p
  34. Midpoint(O, D) → G
  35. Segment(Q, G) → n
  36. Intersect(p, n) → H,
  37. Vector(O, R) → u
  38. Vector(O, D) → v