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Complex Parametric Curves

Complex Parametric Curves
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2019-07-24 14:00
FunctionComplex NumberParametric Equation
This example demonstrates the method of drawing complex parametric curves. It involves core mathematical concepts such as complex numbers and parametric equations. Using GeoGebra commands like CurveCartesian, Sequence, and Element, dynamic drawing of complex parametric curves can be achieved. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, Im(t), Re(t), t, a, b) → curve
  2. Sequence(Segment[(i, 0, 0), curve(i)], i, a, b, eps) → Segmts
  3. Element(listvectordirection, faces) → Selectedvector
  4. Segment((a + ((b - a) * 1 / n), 0, 0), curve(a + ((b - a) * 1 / n))) → A1
  5. Segment((a + ((b - a) * 2 / n), 0, 0), curve(a + ((b - a) * 2 / n))) → A2
  6. Segment((a + ((b - a) * 3 / n), 0, 0), curve(a + ((b - a) * 3 / n))) → A3
  7. Segment((a + ((b - a) * 4 / n), 0, 0), curve(a + ((b - a) * 4 / n))) → A4
  8. Segment((a + ((b - a) * 5 / n), 0, 0), curve(a + ((b - a) * 5 / n))) → A5
  9. Segment((a + ((b - a) * 6 / n), 0, 0), curve(a + ((b - a) * 6 / n))) → A6
  10. Segment((a + ((b - a) * 7 / n), 0, 0), curve(a + ((b - a) * 7 / n))) → A7
  11. Segment((a + ((b - a) * 8 / n), 0, 0), curve(a + ((b - a) * 8 / n))) → A8
  12. Segment((a + ((b - a) * 9 / n), 0, 0), curve(a + ((b - a) * 9 / n))) → A9
  13. Segment((a + ((b - a) * 10 / n), 0, 0), curve(a + ((b - a) * 10 / n))) → A10
  14. Segment((a + ((b - a) * 11 / n), 0, 0), curve(a + ((b - a) * 11 / n))) → A11
  15. Segment((a + ((b - a) * 12 / n), 0, 0), curve(a + ((b - a) * 12 / n))) → A12
  16. Segment((a + ((b - a) * 13 / n), 0, 0), curve(a + ((b - a) * 13 / n))) → A13
  17. Segment((a + ((b - a) * 14 / n), 0, 0), curve(a + ((b - a) * 14 / n))) → A14
  18. Segment((a + ((b - a) * 15 / n), 0, 0), curve(a + ((b - a) * 15 / n))) → A15
  19. Segment((a + ((b - a) * 16 / n), 0, 0), curve(a + ((b - a) * 16 / n))) → A16
  20. Segment((a + ((b - a) * 17 / n), 0, 0), curve(a + ((b - a) * 17 / n))) → A17
  21. Segment((a + ((b - a) * 18 / n), 0, 0), curve(a + ((b - a) * 18 / n))) → A18
  22. Segment((a + ((b - a) * 19 / n), 0, 0), curve(a + ((b - a) * 19 / n))) → A19
  23. Segment((a + ((b - a) * 20 / n), 0, 0), curve(a + ((b - a) * 20 / n))) → A20
  24. Segment((a + ((b - a) * 21 / n), 0, 0), curve(a + ((b - a) * 21 / n))) → A21
  25. Segment((a + ((b - a) * 22 / n), 0, 0), curve(a + ((b - a) * 22 / n))) → A22
  26. Segment((a + ((b - a) * 23 / n), 0, 0), curve(a + ((b - a) * 23 / n))) → A23
  27. Segment((a + ((b - a) * 24 / n), 0, 0), curve(a + ((b - a) * 24 / n))) → A24
  28. Segment((a + ((b - a) * 25 / n), 0, 0), curve(a + ((b - a) * 25 / n))) → A25
  29. Segment((a + ((b - a) * 26 / n), 0, 0), curve(a + ((b - a) * 26 / n))) → A26
  30. Segment((a + ((b - a) * 27 / n), 0, 0), curve(a + ((b - a) * 27 / n))) → A27
  31. Segment((a + ((b - a) * 28 / n), 0, 0), curve(a + ((b - a) * 28 / n))) → A28
  32. Segment((a + ((b - a) * 29 / n), 0, 0), curve(a + ((b - a) * 29 / n))) → A29
  33. Segment((a + ((b - a) * 30 / n), 0, 0), curve(a + ((b - a) * 30 / n))) → A30
  34. Segment((a + ((b - a) * 31 / n), 0, 0), curve(a + ((b - a) * 31 / n))) → A31
  35. Segment((a + ((b - a) * 32 / n), 0, 0), curve(a + ((b - a) * 32 / n))) → A32
  36. Segment((a + ((b - a) * 33 / n), 0, 0), curve(a + ((b - a) * 33 / n))) → A33
  37. Segment((a + ((b - a) * 34 / n), 0, 0), curve(a + ((b - a) * 34 / n))) → A34
  38. Segment((a + ((b - a) * 35 / n), 0, 0), curve(a + ((b - a) * 35 / n))) → A35
  39. Segment((a + ((b - a) * 36 / n), 0, 0), curve(a + ((b - a) * 36 / n))) → A36
  40. Segment((a + ((b - a) * 37 / n), 0, 0), curve(a + ((b - a) * 37 / n))) → A37
  41. Segment((a + ((b - a) * 38 / n), 0, 0), curve(a + ((b - a) * 38 / n))) → A38
  42. Segment((a + ((b - a) * 39 / n), 0, 0), curve(a + ((b - a) * 39 / n))) → A39
  43. Segment((a + ((b - a) * 40 / n), 0, 0), curve(a + ((b - a) * 40 / n))) → A40
  44. Segment((a + ((b - a) * 41 / n), 0, 0), curve(a + ((b - a) * 41 / n))) → A41
  45. Segment((a + ((b - a) * 42 / n), 0, 0), curve(a + ((b - a) * 42 / n))) → A42
  46. Segment((a + ((b - a) * 43 / n), 0, 0), curve(a + ((b - a) * 43 / n))) → A43
  47. Segment((a + ((b - a) * 44 / n), 0, 0), curve(a + ((b - a) * 44 / n))) → A44
  48. Segment((a + ((b - a) * 45 / n), 0, 0), curve(a + ((b - a) * 45 / n))) → A45
  49. Segment((a + ((b - a) * 46 / n), 0, 0), curve(a + ((b - a) * 46 / n))) → A46
  50. Segment((a + ((b - a) * 47 / n), 0, 0), curve(a + ((b - a) * 47 / n))) → A47
  51. Segment((a + ((b - a) * 48 / n), 0, 0), curve(a + ((b - a) * 48 / n))) → A48
  52. Segment((a + ((b - a) * 49 / n), 0, 0), curve(a + ((b - a) * 49 / n))) → A49
  53. Segment((a + ((b - a) * 50 / n), 0, 0), curve(a + ((b - a) * 50 / n))) → A50
  54. Segment((a + ((b - a) * 51 / n), 0, 0), curve(a + ((b - a) * 51 / n))) → A51
  55. Segment((a + ((b - a) * 52 / n), 0, 0), curve(a + ((b - a) * 52 / n))) → A52
  56. Segment((a + ((b - a) * 53 / n), 0, 0), curve(a + ((b - a) * 53 / n))) → A53
  57. Segment((a + ((b - a) * 54 / n), 0, 0), curve(a + ((b - a) * 54 / n))) → A54
  58. Segment((a + ((b - a) * 55 / n), 0, 0), curve(a + ((b - a) * 55 / n))) → A55
  59. Segment((a + ((b - a) * 56 / n), 0, 0), curve(a + ((b - a) * 56 / n))) → A56
  60. Segment((a + ((b - a) * 57 / n), 0, 0), curve(a + ((b - a) * 57 / n))) → A57
  61. Segment((a + ((b - a) * 58 / n), 0, 0), curve(a + ((b - a) * 58 / n))) → A58
  62. Segment((a + ((b - a) * 59 / n), 0, 0), curve(a + ((b - a) * 59 / n))) → A59
  63. Segment((a + ((b - a) * 60 / n), 0, 0), curve(a + ((b - a) * 60 / n))) → A60
  64. Segment((a + ((b - a) * 61 / n), 0, 0), curve(a + ((b - a) * 61 / n))) → A61
  65. Segment((a + ((b - a) * 62 / n), 0, 0), curve(a + ((b - a) * 62 / n))) → A62
  66. Segment((a + ((b - a) * 63 / n), 0, 0), curve(a + ((b - a) * 63 / n))) → A63
  67. Segment((a + ((b - a) * 64 / n), 0, 0), curve(a + ((b - a) * 64 / n))) → A64
  68. Segment((a + ((b - a) * 65 / n), 0, 0), curve(a + ((b - a) * 65 / n))) → A65
  69. Segment((a + ((b - a) * 66 / n), 0, 0), curve(a + ((b - a) * 66 / n))) → A66
  70. Segment((a + ((b - a) * 67 / n), 0, 0), curve(a + ((b - a) * 67 / n))) → A67
  71. Segment((a + ((b - a) * 68 / n), 0, 0), curve(a + ((b - a) * 68 / n))) → A68
  72. Segment((a + ((b - a) * 69 / n), 0, 0), curve(a + ((b - a) * 69 / n))) → A69
  73. Segment((a + ((b - a) * 70 / n), 0, 0), curve(a + ((b - a) * 70 / n))) → A70
  74. Segment((a + ((b - a) * 71 / n), 0, 0), curve(a + ((b - a) * 71 / n))) → A71
  75. Segment((a + ((b - a) * 72 / n), 0, 0), curve(a + ((b - a) * 72 / n))) → A72
  76. Segment((a + ((b - a) * 73 / n), 0, 0), curve(a + ((b - a) * 73 / n))) → A73
  77. Segment((a + ((b - a) * 74 / n), 0, 0), curve(a + ((b - a) * 74 / n))) → A74
  78. Segment((a + ((b - a) * 75 / n), 0, 0), curve(a + ((b - a) * 75 / n))) → A75
  79. Segment((a + ((b - a) * 76 / n), 0, 0), curve(a + ((b - a) * 76 / n))) → A76
  80. Segment((a + ((b - a) * 77 / n), 0, 0), curve(a + ((b - a) * 77 / n))) → A77
  81. Segment((a + ((b - a) * 78 / n), 0, 0), curve(a + ((b - a) * 78 / n))) → A78
  82. Segment((a + ((b - a) * 79 / n), 0, 0), curve(a + ((b - a) * 79 / n))) → A79
  83. Segment((a + ((b - a) * 80 / n), 0, 0), curve(a + ((b - a) * 80 / n))) → A80
  84. Segment((a + ((b - a) * 81 / n), 0, 0), curve(a + ((b - a) * 81 / n))) → A81
  85. Segment((a + ((b - a) * 82 / n), 0, 0), curve(a + ((b - a) * 82 / n))) → A82
  86. Segment((a + ((b - a) * 83 / n), 0, 0), curve(a + ((b - a) * 83 / n))) → A83
  87. Segment((a + ((b - a) * 84 / n), 0, 0), curve(a + ((b - a) * 84 / n))) → A84
  88. Segment((a + ((b - a) * 85 / n), 0, 0), curve(a + ((b - a) * 85 / n))) → A85
  89. Segment((a + ((b - a) * 86 / n), 0, 0), curve(a + ((b - a) * 86 / n))) → A86
  90. Segment((a + ((b - a) * 87 / n), 0, 0), curve(a + ((b - a) * 87 / n))) → A87
  91. Segment((a + ((b - a) * 88 / n), 0, 0), curve(a + ((b - a) * 88 / n))) → A88
  92. Segment((a + ((b - a) * 89 / n), 0, 0), curve(a + ((b - a) * 89 / n))) → A89
  93. Segment((a + ((b - a) * 90 / n), 0, 0), curve(a + ((b - a) * 90 / n))) → A90
  94. Segment((a + ((b - a) * 91 / n), 0, 0), curve(a + ((b - a) * 91 / n))) → A91
  95. Segment((a + ((b - a) * 92 / n), 0, 0), curve(a + ((b - a) * 92 / n))) → A92
  96. Segment((a + ((b - a) * 93 / n), 0, 0), curve(a + ((b - a) * 93 / n))) → A93
  97. Segment((a + ((b - a) * 94 / n), 0, 0), curve(a + ((b - a) * 94 / n))) → A94
  98. Segment((a + ((b - a) * 95 / n), 0, 0), curve(a + ((b - a) * 95 / n))) → A95
  99. Segment((a + ((b - a) * 96 / n), 0, 0), curve(a + ((b - a) * 96 / n))) → A96
  100. Segment((a + ((b - a) * 97 / n), 0, 0), curve(a + ((b - a) * 97 / n))) → A97
  101. Segment((a + ((b - a) * 98 / n), 0, 0), curve(a + ((b - a) * 98 / n))) → A98
  102. Segment((a + ((b - a) * 99 / n), 0, 0), curve(a + ((b - a) * 99 / n))) → A99
  103. Segment((a + ((b - a) * 100 / n), 0, 0), curve(a + ((b - a) * 100 / n))) → A100
  104. Segment((a + ((b - a) * 101 / n), 0, 0), curve(a + ((b - a) * 101 / n))) → A101
  105. Segment((a + ((b - a) * 102 / n), 0, 0), curve(a + ((b - a) * 102 / n))) → A102
  106. Segment((a + ((b - a) * 103 / n), 0, 0), curve(a + ((b - a) * 103 / n))) → A103
  107. Segment((a + ((b - a) * 104 / n), 0, 0), curve(a + ((b - a) * 104 / n))) → A104
  108. Segment((a + ((b - a) * 105 / n), 0, 0), curve(a + ((b - a) * 105 / n))) → A105
  109. Segment((a + ((b - a) * 106 / n), 0, 0), curve(a + ((b - a) * 106 / n))) → A106
  110. Segment((a + ((b - a) * 107 / n), 0, 0), curve(a + ((b - a) * 107 / n))) → A107
  111. Segment((a + ((b - a) * 108 / n), 0, 0), curve(a + ((b - a) * 108 / n))) → A108
  112. Segment((a + ((b - a) * 109 / n), 0, 0), curve(a + ((b - a) * 109 / n))) → A109
  113. Segment((a + ((b - a) * 110 / n), 0, 0), curve(a + ((b - a) * 110 / n))) → A110
  114. Segment((a + ((b - a) * 111 / n), 0, 0), curve(a + ((b - a) * 111 / n))) → A111
  115. Segment((a + ((b - a) * 112 / n), 0, 0), curve(a + ((b - a) * 112 / n))) → A112
  116. Segment((a + ((b - a) * 113 / n), 0, 0), curve(a + ((b - a) * 113 / n))) → A113
  117. Segment((a + ((b - a) * 114 / n), 0, 0), curve(a + ((b - a) * 114 / n))) → A114
  118. Segment((a + ((b - a) * 115 / n), 0, 0), curve(a + ((b - a) * 115 / n))) → A115
  119. Segment((a + ((b - a) * 116 / n), 0, 0), curve(a + ((b - a) * 116 / n))) → A116
  120. Segment((a + ((b - a) * 117 / n), 0, 0), curve(a + ((b - a) * 117 / n))) → A117
  121. Segment((a + ((b - a) * 118 / n), 0, 0), curve(a + ((b - a) * 118 / n))) → A118
  122. Segment((a + ((b - a) * 119 / n), 0, 0), curve(a + ((b - a) * 119 / n))) → A119
  123. Segment((a + ((b - a) * 120 / n), 0, 0), curve(a + ((b - a) * 120 / n))) → A120
  124. Segment((a + ((b - a) * 121 / n), 0, 0), curve(a + ((b - a) * 121 / n))) → A121
  125. Segment((a + ((b - a) * 122 / n), 0, 0), curve(a + ((b - a) * 122 / n))) → A122
  126. Segment((a + ((b - a) * 123 / n), 0, 0), curve(a + ((b - a) * 123 / n))) → A123
  127. Segment((a + ((b - a) * 124 / n), 0, 0), curve(a + ((b - a) * 124 / n))) → A124
  128. Segment((a + ((b - a) * 125 / n), 0, 0), curve(a + ((b - a) * 125 / n))) → A125
  129. Segment((a + ((b - a) * 126 / n), 0, 0), curve(a + ((b - a) * 126 / n))) → A126
  130. Segment((a + ((b - a) * 127 / n), 0, 0), curve(a + ((b - a) * 127 / n))) → A127
  131. Segment((a + ((b - a) * 128 / n), 0, 0), curve(a + ((b - a) * 128 / n))) → A128
  132. Segment((a + ((b - a) * 129 / n), 0, 0), curve(a + ((b - a) * 129 / n))) → A129
  133. Segment((a + ((b - a) * 130 / n), 0, 0), curve(a + ((b - a) * 130 / n))) → A130
  134. Segment((a + ((b - a) * 131 / n), 0, 0), curve(a + ((b - a) * 131 / n))) → A131
  135. Segment((a + ((b - a) * 132 / n), 0, 0), curve(a + ((b - a) * 132 / n))) → A132
  136. Segment((a + ((b - a) * 133 / n), 0, 0), curve(a + ((b - a) * 133 / n))) → A133
  137. Segment((a + ((b - a) * 134 / n), 0, 0), curve(a + ((b - a) * 134 / n))) → A134
  138. Segment((a + ((b - a) * 135 / n), 0, 0), curve(a + ((b - a) * 135 / n))) → A135
  139. Segment((a + ((b - a) * 136 / n), 0, 0), curve(a + ((b - a) * 136 / n))) → A136
  140. Segment((a + ((b - a) * 137 / n), 0, 0), curve(a + ((b - a) * 137 / n))) → A137
  141. Segment((a + ((b - a) * 138 / n), 0, 0), curve(a + ((b - a) * 138 / n))) → A138
  142. Segment((a + ((b - a) * 139 / n), 0, 0), curve(a + ((b - a) * 139 / n))) → A139
  143. Segment((a + ((b - a) * 140 / n), 0, 0), curve(a + ((b - a) * 140 / n))) → A140
  144. Segment((a + ((b - a) * 141 / n), 0, 0), curve(a + ((b - a) * 141 / n))) → A141
  145. Segment((a + ((b - a) * 142 / n), 0, 0), curve(a + ((b - a) * 142 / n))) → A142
  146. Segment((a + ((b - a) * 143 / n), 0, 0), curve(a + ((b - a) * 143 / n))) → A143
  147. Segment((a + ((b - a) * 144 / n), 0, 0), curve(a + ((b - a) * 144 / n))) → A144
  148. Segment((a + ((b - a) * 145 / n), 0, 0), curve(a + ((b - a) * 145 / n))) → A145
  149. Segment((a + ((b - a) * 146 / n), 0, 0), curve(a + ((b - a) * 146 / n))) → A146
  150. Segment((a + ((b - a) * 147 / n), 0, 0), curve(a + ((b - a) * 147 / n))) → A147
  151. Segment((a + ((b - a) * 148 / n), 0, 0), curve(a + ((b - a) * 148 / n))) → A148
  152. Segment((a + ((b - a) * 149 / n), 0, 0), curve(a + ((b - a) * 149 / n))) → A149
  153. Segment((a + ((b - a) * 150 / n), 0, 0), curve(a + ((b - a) * 150 / n))) → A150
  154. Textfield(f) → InputBox1