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Geometric Interpretation of Complex Arithmetic

Geometric Interpretation of Complex Arithmetic
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2019-02-13 17:48
VectorComplex NumberGeometric Construction
This example demonstrates the geometric interpretation of complex arithmetic. It involves core concepts such as addition, subtraction, rotation, and translation of complex numbers. Using GeoGebra commands like If, Textfield, Segment, Vector, etc., it provides a visual understanding of complex numbers. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  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