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Complex Square Roots

Complex Square Roots
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2016-11-25 11:28
FunctionCoordinate GeometryComplex Number
This example illustrates the concept of complex square roots. It demonstrates the properties of complex square roots through geometric representations, involving basic operations and geometric interpretations of complex numbers. Commands such as Shuffle, Element, Min, Max, and Random are used in the construction. Suitable for high school mathematics education and learning about complex numbers.

GeoGebra Commands & Parameters

  1. Shuffle({2, 3, 4, 5, 6, 7, 8, 9}) → numbers
  2. Element(numbers, 5) → e_3
  3. Element(numbers, 8) → f_3
  4. Min({e_3, f_3}) → c_3
  5. Element(Xlist, c_3) → text84
  6. Max({e_3, f_3}) → g_3
  7. Element(Xlist, g_3) → text83
  8. Element(numbers, 4) → b_3
  9. Element(numbers, 3) → a_3
  10. Shuffle({2, 4, 6, 8}) → list1
  11. Element(numbers, 2) → w_2
  12. Element(numbers, 1) → v_2
  13. Element(list1, 2) → j
  14. Element(list1, 1) → e
  15. Random(13, 20) → f_2
  16. Random(3, 12) → v_1
  17. Random(13, 20) → e_2
  18. Random(3, 12) → w_1
  19. Element(Words, l) → text73
  20. Element(Words, j) → text8
  21. Element(Words, e) → text7
  22. Element(Words, k) → text9
  23. Element(list1, 4) → l_3
  24. Element(Words, l_3) → text10
  25. Element(Words, k) → text72
  26. Midpoint(B, D) → H
  27. Midpoint(A, C) → F
  28. Midpoint(F, H) → I
  29. Midpoint(I, H) → R
  30. Midpoint(M_1, N_1) → O_1
  31. Midpoint(O_1, N_1) → Q_1
  32. Midpoint(M_1, O_1) → P_1
  33. Midpoint(F, I) → M
  34. Midpoint(A, B) → E
  35. Midpoint(C, D) → G
  36. Midpoint(E, I) → J
  37. Midpoint(A, F) → K
  38. Midpoint(B, H) → L
  39. Midpoint(K, J) → N
  40. Midpoint(A, E) → O
  41. Midpoint(E, B) → P
  42. Midpoint(J, L) → Q
  43. Midpoint(C, G) → S
  44. Midpoint(G, D) → T
  45. Polygon(U, V, W, Z) → poly1, u, v, w, z_1
  46. Polygon(A_1, B_1, C_1, D_1) → poly2, a_1, b_1, c_1, d_1
  47. Polygon(E_1, F_1, G_1, H_1) → poly3, e_1, f_1, g_1, h_1
  48. Polygon(F, M, P_1, M_1) → poly5, f, m, s, n_1
  49. Polygon(I_1, J_1, K_1, L_1) → poly4, i_1, j_1, k_1, l_1
  50. Polygon(I, R, Q_1, O_1) → poly7, r, t, q_1, s_1
  51. Polygon(M, I, O_1, P_1) → poly6, g, i, m_1, p_1
  52. Polygon(R, H, N_1, Q_1) → poly8, h, r_1, t_1, a_2
  53. Element(list1, 3) → k_3
  54. Shuffle({1, 2, 3, 4}) → Mix
  55. Element(Mix, 1) → n
  56. Element(Mix, 2) → o
  57. Element(Mix, 3) → p
  58. Element(Mix, 4) → q
  59. Element(ShownWords, n) → text11
  60. Element(ShownWords, o) → text12
  61. Element(ShownWords, p) → text13
  62. Element(ShownWords, q) → text14
  63. Element(Definitions, e) → text21
  64. Element(Definitions, j) → text22
  65. LaTeX(Points, true, true) → text25
  66. Polygon(K, M_1, P_1, N) → poly9, k_2, m_2, p_2, n_2
  67. Polygon(N, J, O_1, P_1) → poly10, n_3, j_2, o_1, p_3
  68. Polygon(J, O_1, Q_1, Q) → poly11, j_3, o_2, q_2, q_3
  69. Polygon(Q, Q_1, N_1, L) → poly12, q_4, q_5, n_4, l_2
  70. Textfield(Name) → inputBox1
  71. Textfield(Date) → inputBox2
  72. Segment(R_1, S_1) → b_2
  73. Point(b_2) → T_1
  74. Ellipse(U_1, V_1, T_1) → c_2
  75. Point(c_2) → W_1
  76. Point(c_2) → Z_1
  77. Segment(C_2, D_2) → d_2
  78. Point(d_2) → E_2
  79. Element(Definitions, k) → text23
  80. Element(Definitions, l) → text24
  81. Element(numbers, 6) → d_3
  82. Element(Xlist, h_3) → text85