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Complex Mappings

Complex Mappings
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2017-02-14 14:48
Complex NumberTransformationGeometric ConstructionLocusGraphing
This example demonstrates the geometric representation of complex mappings, visually showing the effects of complex transformations through graphics. It involves core mathematical concepts such as complex numbers, geometric transformations, locus, and analytical geometry. GeoGebra commands and objects like Point, Locus, Polygon, Centroid, and Join are used in the construction. Suitable for high school and above learners to understand the graphical representation and geometric significance of complex function transformations.

GeoGebra Commands & Parameters

  1. SelectedIndex(Namefunctions) → Indexnames
  2. Element(FuncIm, Indexnames) → im
  3. Element(FuncRe, Indexnames) → re
  4. Sequence(Segment[A + (i * (B - A) / a), C + (i * (D - C) / a)], i, 0, a) → list1
  5. Sequence(Segment[A + (i * (C - A) / a), B + (i * (D - B) / a)], i, 0, a) → list2
  6. Point(Element[list1, A1]) → B1
  7. Point(Element[list1, A2]) → B2
  8. Point(Element[list1, A3]) → B3
  9. Point(Element[list1, A4]) → B4
  10. Point(Element[list1, A5]) → B5
  11. Point(Element[list1, A6]) → B6
  12. Point(Element[list1, A7]) → B7
  13. Point(Element[list1, A8]) → B8
  14. Point(Element[list1, A9]) → B9
  15. Point(Element[list1, A10]) → B10
  16. Point(Element[list2, A1]) → C1
  17. Point(Element[list2, A2]) → C2
  18. Point(Element[list2, A3]) → C3
  19. Point(Element[list2, A4]) → C4
  20. Point(Element[list2, A5]) → C5
  21. Point(Element[list2, A6]) → C6
  22. Point(Element[list2, A7]) → C7
  23. Point(Element[list2, A8]) → C8
  24. Point(Element[list2, A9]) → C9
  25. Point(Element[list2, A10]) → C10
  26. Locus(D1, B1) → F1
  27. Locus(D2, B2) → F2
  28. Locus(D3, B3) → F3
  29. Locus(D4, B4) → F4
  30. Locus(D5, B5) → F5
  31. Locus(D6, B6) → F6
  32. Locus(D7, B7) → F7
  33. Locus(D8, B8) → F8
  34. Locus(D9, B9) → F9
  35. Locus(D10, B10) → F10
  36. Locus(E1, C1) → G1
  37. Locus(E2, C2) → G2
  38. Locus(E3, C3) → G3
  39. Locus(E4, C4) → G4
  40. Locus(E5, C5) → G5
  41. Locus(E6, C6) → G6
  42. Locus(E7, C7) → G7
  43. Locus(E8, C8) → G8
  44. Locus(E9, C9) → G9
  45. Locus(E10, C10) → G10
  46. Polygon(A, B, D, C) → poly1, a_1, b, d, c
  47. Point(poly1) → Z
  48. Locus(Z', Z) → loc1
  49. Centroid(poly1) → O
  50. Join({list1, list2}) → list3
  51. Point(list3) → E
  52. If(4 ≤ Indexnames ≤ 6, unites, unitother) → Chooseunit
  53. LaTeX(Indexnames, true, true) → text3
  54. LaTeX(xmax, true, true) → text4
  55. LaTeX(xmin, true, true) → text5
  56. LaTeX(ymax, true, true) → text6
  57. LaTeX(ymin, true, true) → text7