积极 AI Logo 积极 AI

复数根 by Mr Hardman

复数根 by Mr Hardman
几何画板及绘图内容加载中，请稍等……
2015-08-09 07:19
函数解析几何复数
这个范例演示复数根的概念。它涉及复数的几何表示和代数性质。通过使用GeoGebra命令如Sequence、Point、Distance等，可以动态地展示复数根的性质。适合高中数学教学，特别是复数和解析几何的内容。

GeoGebra 命令及参数

  1. Sequence((a^(1 / n) * (cos(((2 * π) * k / n)) + (ί * sin(((2 * π) * k / n))))), k, 1, n) → list2
  2. Point(yAxis) → A
  3. Point(list2) → B
  4. Distance(B, (0, 0)) → f
  5. Textfield(a) → inputBox1
  6. Intersect(xAxis, yAxis) → C
  7. Point(list2) → D
  8. Point(list2) → E
  9. Angle(D, C, E) → α
  10. Intersect(e, xAxis, 2) → F
  11. Point(list2) → G
  12. Point(list2) → H
  13. Point(list2) → I
  14. Point(list2) → J
  15. Angle(Element[list2, n], (0, 0), Element[list2, 1]) → δ
  16. Segment(J, A) → d
  17. Point(list2) → K
  18. Point(list2) → L
  19. Segment(Element[list2, n], (0, 0)) → j
  20. Polygon(list2) → poly1
  21. FractionText(arg(a) / π) → text10
  22. FractionText(θ) → text11
  23. FractionText(2 / n) → text12
  24. FractionText(Element[list4, 1]) → text14
  25. FractionText(Element[list4, 2]) → text15
  26. FractionText(Element[list4, 3]) → text16
  27. FractionText(Element[list4, 4]) → text20
  28. FractionText(Element[list4, 5]) → text21
  29. FractionText(Element[list4, 6]) → text22
  30. FractionText(Element[list4, 7]) → text23
  31. FractionText(Element[list4, 8]) → text24
  32. FractionText(Element[list4, 9]) → text25
  33. FractionText(Element[list4, 10]) → text26
  34. Sequence((a_1^(1 / n) * (cos(((2 * π) * k / n)) + (ί * sin(((2 * π) * k / n))))), k, 1, n) → list2_1
  35. Point(list2_1) → B_1
  36. Textfield(a_1) → inputBox1_1
  37. Point(list2_1) → D_1
  38. Point(list2_1) → E_1
  39. Point(list2_1) → G_1
  40. Point(list2_1) → H_1
  41. Point(list2_1) → I_1
  42. Point(list2_1) → J_1
  43. Point(list2_1) → K_1
  44. Point(list2_1) → L_1
  45. Polygon(list2_1) → poly1_1
  46. FractionText(Element[list4_1, 3]) → text16_1
  47. Sequence((a_2^(1 / n) * (cos(((2 * π) * k / n)) + (ί * sin(((2 * π) * k / n))))), k, 1, n) → list2_2
  48. Point(list2_2) → B_2
  49. Textfield(a_2) → inputBox1_2
  50. Point(list2_2) → D_2
  51. Point(list2_2) → E_2
  52. Point(list2_2) → G_2
  53. Point(list2_2) → H_2
  54. Point(list2_2) → I_2
  55. Point(list2_2) → J_2
  56. Point(list2_2) → K_2
  57. Point(list2_2) → L_2
  58. Polygon(list2_2) → poly1_2
  59. FractionText(Element[list4_2, 4]) → text20_1
  60. Sequence((a_3^(1 / n) * (cos(((2 * π) * k / n)) + (ί * sin(((2 * π) * k / n))))), k, 1, n) → list2_3
  61. Point(list2_3) → B_3
  62. Textfield(a_3) → inputBox1_3
  63. Point(list2_3) → D_3
  64. Point(list2_3) → E_3
  65. Point(list2_3) → G_3
  66. Point(list2_3) → H_3
  67. Point(list2_3) → I_3
  68. Point(list2_3) → J_3
  69. Point(list2_3) → K_3
  70. Point(list2_3) → L_3
  71. Polygon(list2_3) → poly1_3
  72. FractionText(Element[list4_3, 6]) → text22_1
  73. Sequence((a_4^(1 / n) * (cos(((2 * π) * k / n)) + (ί * sin(((2 * π) * k / n))))), k, 1, n) → list2_4
  74. Point(list2_4) → B_4
  75. Textfield(a_4) → inputBox1_4
  76. Point(list2_4) → D_4
  77. Point(list2_4) → E_4
  78. Point(list2_4) → G_4
  79. Point(list2_4) → H_4
  80. Point(list2_4) → I_4
  81. Point(list2_4) → J_4
  82. Point(list2_4) → K_4
  83. Point(list2_4) → L_4
  84. Polygon(list2_4) → poly1_4
  85. FractionText(Element[list4_4, 6]) → text22_2
  86. Sequence((a_5^(1 / n) * (cos(((2 * π) * k / n)) + (ί * sin(((2 * π) * k / n))))), k, 1, n) → list2_5
  87. Point(list2_5) → B_5
  88. Textfield(a_5) → inputBox1_5
  89. Point(list2_5) → D_5
  90. Point(list2_5) → E_5
  91. Point(list2_5) → G_5
  92. Point(list2_5) → H_5
  93. Point(list2_5) → I_5
  94. Point(list2_5) → J_5
  95. Point(list2_5) → K_5
  96. Point(list2_5) → L_5
  97. Polygon(list2_5) → poly1_5
  98. FractionText(Element[list4_5, 7]) → text23_1
  99. Sequence((a_6^(1 / n) * (cos(((2 * π) * k / n)) + (ί * sin(((2 * π) * k / n))))), k, 1, n) → list2_6
  100. Point(list2_6) → B_6
  101. Textfield(a_6) → inputBox1_6
  102. Point(list2_6) → D_6
  103. Point(list2_6) → E_6
  104. Point(list2_6) → G_6
  105. Point(list2_6) → H_6
  106. Point(list2_6) → I_6
  107. Point(list2_6) → J_6
  108. Point(list2_6) → K_6
  109. Point(list2_6) → L_6
  110. Polygon(list2_6) → poly1_6
  111. FractionText(Element[list4_6, 8]) → text24_1
  112. Sequence((a_7^(1 / n) * (cos(((2 * π) * k / n)) + (ί * sin(((2 * π) * k / n))))), k, 1, n) → list2_7
  113. Point(list2_7) → B_7
  114. Textfield(a_7) → inputBox1_7
  115. Point(list2_7) → D_7
  116. Point(list2_7) → E_7
  117. Point(list2_7) → G_7
  118. Point(list2_7) → H_7
  119. Point(list2_7) → I_7
  120. Point(list2_7) → J_7
  121. Point(list2_7) → K_7
  122. Point(list2_7) → L_7
  123. Polygon(list2_7) → poly1_7
  124. FractionText(Element[list4_7, 10]) → text25_1
  125. Vector((0, 0), a) → u

AI 绘图提示语参考

绘制一个复数的n次根的几何表示。首先在实轴上取一个点A，然后根据给定的复数a和n次根的定义，生成n个复数根并依次绘制在复平面上，形成一个正多边形。接着计算每个根与原点之间的距离f，并标出角度α。绘制从原点到每个根的线段，并计算每个根与相邻根之间的角度δ。最后，绘制一个包含所有根的多边形，并标注每个根的幅角。
以上提示语为根据原始绘图命令整理而来，仅供参考。