复数i的几何表示与单位圆关系探究

GeoGebra 命令及参数

1. Vector((0, 0), (1, 0)) → u
2. Vector((0, -0.007890188248790508), (a^(0.5), a^(0.5))) → d
3. Vector((0, 0), ((-a^(0.5)), (-a^(0.5)))) → e
4. Vector((0, 0), (a^(0.5), (-a^(0.5)))) → f
5. Vector((0, 0), ((-a^(0.5)), a^(0.5))) → g
6. Point(b) → C
7. Point(v) → D
8. Point(w) → E
9. Point(c) → F
10. Point(d) → G
11. Point(e) → H
12. Point(g) → I
13. Point(f) → J
14. Point(f) → K
15. Line(G, w) → h
16. Point(v) → L
17. Vector((0, 0), (a^(0.5), 0)) → i
18. Point(i) → M
19. Segment(M, G) → j
20. Segment(D, E) → k
21. Segment(E, C) → l
22. Segment(C, F) → m
23. Segment(F, D) → n
24. Segment(G, I) → p
25. Segment(I, H) → q
26. Segment(H, J) → r
27. Segment(J, M) → s
28. Point(k) → A
29. Distance(K, A) → distanceKA
30. Distance(G, K) → distanceGK
31. Point(v) → B
32. Distance(B, A) → distanceBA
33. Segment(B, A) → t_x
34. Circle(K, H) → c_1
35. Circle(K, C) → d_1
36. Segment(I, J) → a_1
37. Mirror(e, a_1) → e'
38. Mirror(M, p) → M'
39. Mirror(G, p) → G'
40. Segment(M', G') → j'
41. Distance(M, M') → distanceMM'
42. Polygon(K, E, A) → poly1, a_2, k_1, e_2
43. Point(d_1) → N
44. Point(d_1) → O
45. Segment(N, O) → b_1
46. Factors(o) → matrix1
47. ReducedRowEchelonForm(matrix1) → matrix2
48. Segment(E, M') → h_1
49. Point(Circle[E, 1.16]) → P
50. Segment(E, P) → g_1
51. Point(Circle[P, 1.16]) → Q
52. Segment(P, Q) → i_1
53. Point(Circle[E, 1.64]) → R
54. Segment(E, R) → j_1
55. Angle(M', E, R) → α
56. Point(Circle[M', 1.16]) → S
57. Segment(M', S) → l_1
58. Point(Circle[E, 1.16]) → T
59. Segment(E, T) → m_1
60. CircleArc(K, I, H) → p_1
61. CircleArc(K, H, G) → e_1
62. CircleArc(K, E, I) → q_1
63. Intersect(j', h_1) → V
64. Point(Circle[M, 1.64]) → W
65. Segment(M, W) → r_1
66. Point(Circle[W, 1.16]) → Z
67. Segment(W, Z) → s_1
68. Point(Circle[Z, 1.16]) → A_1
69. Segment(Z, A_1) → t_1
70. Segment(T, V) → b_2
71. Segment(D, T) → c_2
72. Point(m_1) → B_1
73. Segment(E, B_1) → d_2
74. Segment(Z, T) → f_2
75. Polygon(E, T, Z) → poly2, z_1, e_3, t_2
76. Polygon(D, W, Z, T) → poly3, d_3, w_1, z_2, t_3
77. Intersect(t_x, k_1) → C_1
78. Point(Circle[E, 0.72]) → D_1
79. Segment(E, D_1) → h_2
80. Point(t_x) → E_1
81. Point(Circle[E, 1.41]) → F_1
82. Segment(E, F_1) → i_2
83. Segment(E, Z) → j_2
84. Mirror(E, k_2) → E'
85. Mirror(M', k_2) → M''
86. Segment(E', M'') → l_2
87. Mirror(M', k_2) → M''_1
88. Mirror(S, k_2) → S'
89. Segment(M''_1, S') → m_2
90. Mirror(M', k_2) → M''_2
91. Mirror(G', k_2) → G''
92. Segment(M''_2, G'') → j''
93. Mirror(D, k_2) → D'
94. Mirror(T, k_2) → T'
95. Segment(D', T') → n_2
96. Mirror(Z, k_2) → Z'
97. Mirror(T, k_2) → T'_1
98. Segment(Z', T'_1) → p_2
99. Mirror(E, k_2) → E'_1
100. Mirror(Z, k_2) → Z'_1
101. Segment(E'_1, Z'_1) → q_2
102. Mirror(B, k_2) → B'
103. Mirror(A, k_2) → A'
104. Segment(B', A') → r_2
105. Mirror(E, k_2) → E'_2
106. Mirror(F_1, k_2) → G_1
107. Segment(E'_2, G_1) → s_2
108. Mirror(M, k_2) → M'_1
109. Mirror(G, k_2) → G'_1
110. Segment(M'_1, G'_1) → j'_1
111. Mirror(W, k_2) → W'
112. Mirror(D, k_2) → D'_1
113. Mirror(W, k_2) → W'_1
114. Mirror(Z, k_2) → Z'_2
115. Mirror(E, k_2) → E'_3
116. Mirror(T, k_2) → T'_2
117. Segment(E'_3, T'_2) → g_2
118. Mirror(E, k_2) → E'_4
119. Mirror(B_1, k_2) → H_1
120. Segment(E'_4, H_1) → a_3
121. Point(s_2) → I_1
122. Point(i_2) → J_1
123. Segment(I_1, J_1) → b_3
124. Mirror(E, k_2) → E'_5
125. Mirror(D_1, k_2) → K_1
126. Segment(E'_5, K_1) → c_3