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Basic Operations with Complex Numbers

Basic Operations with Complex Numbers
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2017-03-04 10:12
VectorCoordinate GeometryComplex Number
This example demonstrates basic operations with complex numbers, including addition, subtraction, multiplication, and division. By inputting the real and imaginary parts of complex numbers, you can see the results visually. It uses commands like If, Textfield, Segment, Vector, etc., suitable for students at the junior high school level and above.

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