MathPlotAI Logo MathPlotAI

Geometric Demo of Complex Numbers a,b with |a|<1 & |b|<1

Geometric Demo of Complex Numbers a,b with |a|<1 & |b|<1
Loading the math board and drawing, please wait…
2017-06-12 20:43
Complex NumberTransformationGeometric Construction
This example demonstrates the geometric representation and transformation of complex numbers a,b where |a|<1 and |b|<1. Key math concepts include complex numbers, modulus, geometric transformations, and inequalities. It is constructed using GeoGebra commands such as Mirror, Intersect, Vector, OrthogonalLine, Line, Segment, Point, Circle, Angle, Rotate, and Ray. Suitable for high school mathematics education to understand the geometric meaning and applications of complex number transformations.

GeoGebra Commands & Parameters

  1. Mirror(A, xAxis) → A'
  2. Intersect(xAxis, yAxis) → C_1
  3. Vector(C_1, A') → u
  4. Vector(C_1, B) → v
  5. Vector(C_1, A) → a
  6. OrthogonalLine(C_1, v) → f
  7. Mirror(B, f) → B'
  8. Line(A, w) → g
  9. Line(B', a) → h
  10. Intersect(g, h) → D
  11. Segment(D, C_1) → i
  12. Point(yAxis) → E
  13. Circle(C_1, E) → c
  14. Intersect(c, xAxis, 2) → F
  15. Angle(F, C_1, B) → α
  16. Angle(F, C_1, A') → β
  17. Rotate(F, α + β, C_1) → F'
  18. Angle(F, C_1, F') → γ
  19. Ray(C_1, F') → j
  20. Segment(C_1, B) → k
  21. Segment(C_1, A') → l
  22. Point(Circle[C_1, s]) → G
  23. Segment(C_1, G) → m
  24. Circle(C_1, G) → d
  25. Intersect(d, j, 1) → H
  26. Rotate(H, 180°, C_1) → H'
  27. Vector(C_1, H') → b
  28. Vector(C_1, F) → e
  29. Line(H', e) → n
  30. Line(F, b) → p
  31. Intersect(n, p) → C
  32. Segment(C_1, C) → q
  33. Circle(C_1, C) → r
  34. Circle(C_1, D) → t