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i Geometry Dimensions Demo

i Geometry Dimensions Demo
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2016-01-13 13:29
CircleVectorComplex NumberGeometric Construction
This example demonstrates the geometric representation of the complex unit 'i' on the complex plane and its relationship with the unit circle. It involves core math concepts like complex numbers, unit circle, vectors, and geometric transformations. Construction highlights include commands like Vector, Point, Line, Segment, Distance, Circle, Mirror, Polygon, Factors, ReducedRowEchelonForm, Angle, CircleArc, Intersect. Suitable for high school and above learners to understand the geometric meaning and manipulation of complex numbers.

GeoGebra Commands & Parameters

  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