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复数运算 by Luis Miguel López Herranz

复数运算 by Luis Miguel López Herranz
几何画板及绘图内容加载中，请稍等……
2015-01-07 22:48
解析几何复数几何作图
本范例展示了复数在极坐标和直角坐标形式下的所有运算。它涉及复数的基本概念，如加法、减法、乘法和除法。通过使用GeoGebra命令如Point、Intersect、Angle等，可以直观地理解复数运算的几何意义。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Point(xAxis) → N_2
  2. Intersect(xAxis, yAxis) → F_2
  3. Angle(N_2, F_2, z_{14}) → β
  4. Segment(z_{14}, F_2) → m_4
  5. Point(Circle[A, 3]) → B
  6. Segment(A, B) → a
  7. Point(Circle[B, 1.5]) → C
  8. Segment(B, C) → b
  9. Point(Circle[C, 1.5]) → D
  10. Segment(C, D) → c
  11. Point(Circle[D, 1.5]) → E
  12. Segment(D, E) → d
  13. Point(Circle[E, 1.5]) → F
  14. Segment(E, F) → e
  15. Point(Circle[F, 1.5]) → G
  16. Segment(F, G) → f
  17. OrthogonalLine(A, a) → g
  18. Circle(A, 0.75) → h
  19. Intersect(h, g, 2) → H
  20. Circle(H, 0.75) → k
  21. Intersect(k, g, 2) → I
  22. OrthogonalLine(H, g) → i
  23. OrthogonalLine(I, g) → j
  24. OrthogonalLine(B, a) → l
  25. OrthogonalLine(C, b) → m
  26. OrthogonalLine(D, c) → n
  27. OrthogonalLine(E, d) → p
  28. OrthogonalLine(F, e) → q
  29. OrthogonalLine(G, f) → r
  30. Circle(I, 0.75) → s
  31. Intersect(s, g, 2) → J
  32. OrthogonalLine(J, g) → t
  33. Intersect(j, l) → K
  34. Intersect(l, t) → L
  35. Intersect(m, t) → M
  36. Intersect(n, t) → N
  37. Intersect(p, t) → O
  38. Intersect(q, t) → P
  39. Intersect(r, t) → Q
  40. Intersect(j, r) → R
  41. Intersect(j, q) → S
  42. Intersect(j, p) → T
  43. Intersect(j, n) → U
  44. Intersect(j, m) → V
  45. Intersect(i, m) → W
  46. Intersect(i, l) → Z
  47. Intersect(i, n) → A_1
  48. Intersect(i, p) → B_1
  49. Intersect(i, q) → C_1
  50. Intersect(i, r) → D_1
  51. Midpoint(M, K) → E_1
  52. Midpoint(N, V) → F_1
  53. Midpoint(O, U) → G_1
  54. Midpoint(P, T) → H_1
  55. Midpoint(Q, S) → I_1
  56. Midpoint(R, C_1) → J_1
  57. Midpoint(D_1, F) → K_1
  58. Midpoint(C_1, E) → L_1
  59. Midpoint(B_1, D) → M_1
  60. Midpoint(T, A_1) → N_1
  61. Midpoint(U, W) → O_1
  62. Midpoint(A_1, C) → P_1
  63. Midpoint(W, B) → Q_1
  64. Midpoint(V, Z) → R_1
  65. Midpoint(K, H) → S_1
  66. Midpoint(Z, A) → T_1
  67. Polygon(R, Q, P, S) → polígono1, r_1, q_1, p_1, s_1
  68. Polygon(S, K, L, P) → polígono2, s_2, k_1, l_1, p_2
  69. Segment(L, K) → a_1
  70. Segment(L, Q) → b_1
  71. Segment(Q, R) → c_1
  72. Segment(R, K) → d_1
  73. Segment(P, S) → e_1
  74. Midpoint(S, B_1) → U_1
  75. Polygon(I, K, Z, H) → polígono3, i_1, k_2, z_1, h_1
  76. Polygon(H, A, B, Z) → polígono4, h_2, a_2, b_2, z_2
  77. Segment(Z, D_1) → f_1
  78. Segment(R, G) → g_1
  79. Segment(S, F) → j_1
  80. Segment(O, E) → m_1
  81. Segment(N, D) → n_1
  82. Segment(M, C) → t_1
  83. Polygon(K, Z, W, V) → polígono5, k_3, z_3, w, v
  84. Polygon(V, W, A_1, U) → polígono6, v_1, w_1, a_3, u
  85. Polygon(U, A_1, B_1, T) → polígono7, u_1, a_4, b_3, t_2
  86. Polygon(T, B_1, C_1, S) → polígono8, t_3, b_4, c_2, s_3
  87. Polygon(C_1, D_1, R, S) → polígono9, c_3, d_2, r_2, s_4
  88. Polygon(C_1, F, G, D_1) → polígono10, c_4, f_2, g_2, d_3
  89. Polygon(F, E, B_1, C_1) → polígono11, f_3, e_2, b_5, c_5
  90. Polygon(E, D, A_1, B_1) → polígono12, e_3, d_4, a_5, b_6
  91. Polygon(D, C, W, A_1) → polígono13, d_5, c_6, w_2, a_6
  92. Polygon(C, B, Z, W) → polígono14, c_7, b_7, z_4, w_3
  93. Mirror(C_1, g_1) → V_1
  94. Mirror(F, g_1) → F'
  95. Mirror(G, g_1) → G'
  96. Mirror(D_1, g_1) → W_1
  97. Polygon(V_1, F', G', W_1) → polígono10', v_2, f', g', w_4
  98. Mirror(C_1, g_1) → Z_1
  99. Mirror(D_1, g_1) → A_2
  100. Mirror(R, g_1) → R'
  101. Mirror(S, g_1) → S'
  102. Polygon(Z_1, A_2, R', S') → polígono9', z_5, a_7, r', s'
  103. Mirror(Z_1, r') → B_2
  104. Mirror(A_2, r') → C_2
  105. Mirror(R', r') → R''
  106. Mirror(S', r') → S''
  107. Polygon(B_2, C_2, R'', S'') → polígono9'', b_8, c_8, r'', s''
  108. Mirror(K_1, g_1) → D_2
  109. Mirror(D_2, w_4) → E_2
  110. Textfield(z_6) → CasillaDeEntrada1
  111. Textfield(z_7) → CasillaDeEntrada2
  112. Segment(F_2, z_{9}) → q_2
  113. Segment(F_2, z_{10}) → g_3
  114. Segment(z_{11}, F_2) → h_3
  115. Textfield(u_2) → CasillaDeEntrada3
  116. Segment(z_{13}, F_2) → i_3
  117. Point(xAxis) → G_2
  118. Angle(G_2, F_2, z_6) → α
  119. Textfield(n_3) → CasillaDeEntrada4
  120. OrthogonalLine(z_6, xAxis) → l_3
  121. OrthogonalLine(z_7, xAxis) → m_3
  122. OrthogonalLine(z_6, yAxis) → p_3
  123. OrthogonalLine(z_7, yAxis) → q_3
  124. Intersect(q_3, yAxis) → H_2
  125. Intersect(p_3, yAxis) → I_2
  126. Intersect(m_3, xAxis) → J_2
  127. Intersect(l_3, xAxis) → K_2
  128. OrthogonalLine(z_8, xAxis) → r_3
  129. OrthogonalLine(z_8, yAxis) → e_4
  130. Intersect(r_3, xAxis) → L_2
  131. Intersect(e_4, yAxis) → M_2
  132. Segment(F_2, K_2) → f_4
  133. Vector(H_2, z_7) → u_3
  134. Vector(K_2, L_2) → v_3
  135. Vector(J_2, z_7) → u_4
  136. Vector(I_2, M_2) → i_2
  137. Segment(F_2, I_2) → j_2
  138. Segment(z_8, L_2) → l_2
  139. Segment(z_8, M_2) → g_4
  140. Segment(z_6, K_2) → h_4
  141. Segment(z_6, I_2) → i_4
  142. Segment(z_7, H_2) → j_4
  143. Segment(z_7, J_2) → k_4
  144. Segment(F_2, z_6) → l_4
  145. Sequence(((l_4^(1 / n_3) * cos(α / n_3 + (360° * i / n_3))), (l_4^(1 / n_3) * sin(α / n_3 + (360° * i / n_3)))), i, 0, n_3 - 1) → lista1
  146. Sequence((m_4^(1 / n_3); β / n_3 + (360° * i / n_3)), i, 0, n_3 - 1) → lista2
  147. Textfield(z_{14}) → CasillaDeEntrada5
  148. Segment(z_{15}, F_2) → n_4
  149. Angle(N_2, F_2, z_{15}) → γ
  150. Sequence(Segment[((l_4^(1 / n_3) * cos(α / n_3 + (360° * i / n_3))), (l_4^(1 / n_3) * sin(α / n_3 + (360° * i / n_3)))), ((l_4^(1 / n_3) * cos(α / n_3 + (360° * (i + 1) / n_3))), (l_4^(1 / n_3) * sin(α / n_3 + (360° * (i + 1) / n_3))))], i, 0, n_3 - 1) → lista3
  151. Textfield(z_{15}) → CasillaDeEntrada6
  152. Segment(O_2, P_2) → p_4
  153. Segment(Q_2, F_2) → q_4
  154. Angle(N_2, F_2, Q_2) → δ
  155. OrthogonalLine(z_{9}, xAxis) → r_4
  156. OrthogonalLine(z_{9}, yAxis) → t_4
  157. Intersect(r_4, xAxis) → R_2
  158. Intersect(t_4, yAxis) → S_2
  159. Segment(z_{9}, R_2) → e_5
  160. Segment(z_{9}, S_2) → f_5
  161. Segment(F_2, z_{19}) → g_5
  162. Angle(N_2, F_2, z_{19}) → ε
  163. Segment(z_{21}, F_2) → h_5
  164. Angle(N_2, F_2, z_{14}) → ζ
  165. Angle(N_2, F_2, z_{15}) → η
  166. Angle(N_2, F_2, z_{14}) → κ
  167. Angle(N_2, F_2, z_{15}) → λ
  168. Segment(z_{23}, F_2) → i_5
  169. Angle(z_{23}, F_2, z_{14}) → μ
  170. Angle(N_2, F_2, z_{23}) → ν
  171. Segment(z_{24}, F_2) → j_5
  172. Angle(N_2, F_2, z_{24}) → ξ
  173. Sequence(Angle[N_2, (0, 0), (m_4 / 2; (β * i))], i, 1, u_2) → lista4
  174. Sequence((m_4; (β * i)), i, 1, u_2) → lista6
  175. Sequence(Segment[(m_4^(1 / n_3); β / n_3 + (360° * i / n_3)), (m_4^(1 / n_3); β / n_3 + (360° * (1 + i) / n_3))], i, 0, n_3 - 1) → lista7
  176. Sequence(CircumcircleArc[(m_4, 0), (m_4; (β * i)), (m_4; (β * (1 + i)))], i, 1, u_2 - 1) → lista5
  177. OrthogonalLine(z_{9}, xAxis) → k_5
  178. Intersect(xAxis, k_5) → T_2
  179. Segment(T_2, z_{9}) → l_5
  180. Angle(z_{14}, F_2, z_{21}) → θ