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复数运算的几何解释

复数运算的几何解释
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2019-02-13 17:48
向量复数几何作图
这个范例演示了复数运算的几何解释。它涉及复数的加减法、旋转和平移等核心数学概念。通过使用GeoGebra命令如If, Textfield, Segment, Vector等，可以直观地展示复数的几何意义。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. If(form ≟ true, ((const1 * x(Apolar)) + (const2 * x(Bpolar)), (const1 * y(Apolar)) + (const2 * y(Bpolar))), ((const1 * a) + (const2 * c), (const1 * b) + (const2 * d))) → Z5
  2. If(form ≟ true, (((x(Apolar) * x(Bpolar)) + (y(Apolar) * y(Bpolar))) / (x(Bpolar)^(2) + y(Bpolar)^(2)), ((y(Apolar) * x(Bpolar)) - (x(Apolar) * y(Bpolar))) / (x(Bpolar)^(2) + y(Bpolar)^(2))), (((a * c) + (b * d)) / (c^(2) + d^(2)), ((b * c) - (a * d)) / (c^(2) + d^(2)))) → Z4
  3. If(form ≟ true, ((x(Apolar) * x(Bpolar)) - (y(Apolar) * y(Bpolar)), (y(Apolar) * x(Bpolar)) + (x(Apolar) * y(Bpolar))), ((a * c) - (b * d), (b * c) + (a * d))) → Z3
  4. If(form ≟ true, (x(Apolar) - x(Bpolar), y(Apolar) - y(Bpolar)), (a - c, b - d)) → Z2
  5. Textfield(xA) → InputBox1
  6. Textfield(yA) → InputBox2
  7. Textfield(xB) → InputBox3
  8. Textfield(yB) → InputBox4
  9. Segment((0, 0), A) → rA
  10. Segment((0, 0), B) → rB
  11. If(form ≟ true, (x(Apolar) + x(Bpolar), y(Apolar) + y(Bpolar)), (a + c, b + d)) → Z1
  12. Segment((0, 0), Z1) → rZ1
  13. Segment((0, 0), Z2) → rZ2
  14. Segment((0, 0), Z3) → rZ3
  15. Segment((0, 0), Z4) → rZ4
  16. Vector((0, 0), A) → uA
  17. Vector((0, 0), B) → uB
  18. Vector((0, 0), Z1) → uZ1
  19. Vector((0, 0), Z2) → uZ2
  20. Vector((0, 0), Z3) → uZ3
  21. Vector((0, 0), Z4) → uZ4
  22. SelectedIndex(operation) → indexop
  23. Angle((1000, 0), (0, 0), Element[points, indexop]) → ε
  24. Angle(Element[points, indexop], (0, 0), (1000, 0)) → ζ
  25. Segment(B', Z1) → f
  26. Segment(A', Z1) → g
  27. Vector((0, 0), A') → uA'
  28. Vector((0, 0), B') → uB'
  29. Mirror(uB', (0, 0)) → uB''
  30. Segment(A', Z2) → h
  31. Segment(Z2, Bminus) → i
  32. Textfield(guessx) → InputBox5
  33. Textfield(guessy) → InputBox6
  34. Ray((0, 0), Element[points, indexop]) → Rayz
  35. Vector((0, 0), Z5) → uZ5
  36. Vector((0, 0), A'') → uA''
  37. Vector((0, 0), B'') → uB3
  38. Vector((0, 0), A) → u
  39. Vector((0, 0), B) → v
  40. Textfield(const1) → InputBox7
  41. Textfield(const2) → InputBox8
  42. Segment(Z5, A'') → j
  43. Segment(Z5, B'') → k
  44. Angle((1000, 0), (0, 0), Apolar) → α
  45. Angle(Apolar, (0, 0), (1000, 0)) → β
  46. Angle((1000, 0), (0, 0), Bpolar) → γ
  47. Angle(Bpolar, (0, 0), (1000, 0)) → δ
  48. If(form ≟ true, (x(Apolar) + x(Bpolar), y(Apolar) + y(Bpolar)), (a + c, b + d)) → ZZ
  49. Vector((0, 0), Apolar) → upolar
  50. Vector((0, 0), Bpolar) → vpolar
  51. Vector((0, 0), Apolar') → w
  52. Vector((0, 0), Bpolar') → e
  53. Vector((0, 0), Apolar) → l
  54. Vector((0, 0), Bpolar) → m
  55. Vector((0, 0), Bpolarminus) → n
  56. Textfield(theta1) → InputBox9
  57. Textfield(theta2) → InputBox11
  58. Textfield(mod1) → InputBox10
  59. Textfield(mod2) → InputBox12
  60. Line(C, xAxis) → p
  61. Line(D, p) → q
  62. Segment((0, 0), Z5) → rZ5
  63. Segment(Bpolar', Z5) → r
  64. Segment(Apolar', Z5) → s
  65. TableText({{LaTeX[A, true, true]}, {LaTeX[B, true, true]}}) → CartesianPoints
  66. TableText({{LaTeX[Apolar, true, true]}, {LaTeX[Bpolar, true, true]}}) → PolarPoints