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Complex Trigonometry

Complex Trigonometry
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2018-01-13 01:45
TrigonometryCoordinate GeometryComplex NumberGeometric Construction
This example demonstrates the integration of complex numbers and trigonometric functions through dynamic geometry, illustrating the geometric meaning of complex numbers and properties of trigonometric functions. Key concepts include complex numbers, trigonometric functions, circles, vectors, and coordinate geometry. Construction highlights the use of GeoGebra commands like Vector, Point, Segment, Line, OrthogonalLine, Intersect, and Mirror. Suitable for high school and above, aiding in understanding complex planes, trigonometric graphs, and geometric transformations.

GeoGebra Commands & Parameters

  1. Vector((a, 0)) → u
  2. Vector((a, 0), (a, b)) → v
  3. Vector((a, 0), (a, c)) → w
  4. Point(w) → E
  5. Segment(C, E) → l
  6. Point(v) → F
  7. Segment(C, F) → m
  8. Vector((b, 0), (b, f)) → n
  9. Vector((b, 0), (b, g)) → p
  10. Point(p) → G
  11. Point(n) → D
  12. Segment(C, G) → j
  13. Segment(C, D) → k
  14. Point(u) → I
  15. Line(G, j) → q
  16. Line(F, w) → r
  17. Point(q) → J
  18. Point(u) → K
  19. OrthogonalLine(J, xAxis) → d_1
  20. Intersect(s, t) → P
  21. Segment(C, P) → a_1
  22. Intersect(t, yAxis) → Q
  23. Segment(Q, P) → b_1
  24. Segment(T, P) → c_1
  25. Segment(S, A_1) → e_1
  26. Segment(R, Z) → f_1
  27. Segment(U, B_1) → g_1
  28. Segment(V, C_1) → h_1
  29. Segment(C, W) → i_1
  30. Mirror(C, c_1) → C'
  31. Mirror(W, c_1) → W'
  32. Segment(C', W') → j_1
  33. Mirror(R, c_1) → R'
  34. Mirror(Z, c_1) → Z'
  35. Segment(R', Z') → k_1
  36. Mirror(S, c_1) → S'
  37. Mirror(A_1, c_1) → D_1
  38. Segment(S', D_1) → l_1
  39. Mirror(Q, c_1) → Q'
  40. Mirror(P, c_1) → P'
  41. Segment(Q', P') → m_1
  42. Mirror(V, c_1) → V'
  43. Mirror(C_1, c_1) → E_1
  44. Segment(V', E_1) → n_1
  45. Mirror(U, c_1) → U'
  46. Mirror(B_1, c_1) → F_1
  47. Segment(U', F_1) → p_1
  48. Mirror(S', j_1) → S''
  49. Mirror(D_1, j_1) → G_1
  50. Segment(S'', G_1) → q_1
  51. Mirror(R', j_1) → R''
  52. Mirror(Z', j_1) → Z''
  53. Segment(R'', Z'') → r_1
  54. Mirror(Q', j_1) → Q''
  55. Mirror(P', j_1) → P''
  56. Segment(Q'', P'') → s_1
  57. Mirror(V', j_1) → V''
  58. Mirror(E_1, j_1) → H_1
  59. Segment(V'', H_1) → t_1
  60. Mirror(U', j_1) → U''
  61. Mirror(F_1, j_1) → I_1
  62. Segment(U'', I_1) → a_2
  63. Mirror(S'', s_1) → S'''
  64. Mirror(G_1, s_1) → K_1
  65. Segment(S''', K_1) → b_2
  66. Mirror(V'', s_1) → V'''
  67. Mirror(H_1, s_1) → J_1
  68. Segment(V''', J_1) → c_2
  69. Mirror(U'', s_1) → U'''
  70. Mirror(I_1, s_1) → L_1
  71. Segment(U''', L_1) → d_2
  72. Mirror(R'', s_1) → R'''
  73. Mirror(Z'', s_1) → Z'''
  74. Segment(R''', Z''') → e_2
  75. Segment(C, E) → f_2
  76. Segment(C, F) → g_2