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Demonstrating X+Y+Z using Complex Numbers

Demonstrating X+Y+Z using Complex Numbers
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2017-04-22 07:41
VectorComplex NumberGeometric Construction
This example demonstrates the geometric interpretation of X+Y+Z using complex numbers. It involves core math concepts like complex numbers, vectors, angles, and geometric constructions. GeoGebra commands used include Intersect, Vector, Point, Angle, Sequence, and If. Suitable for high school and above, helping learners understand the connection between complex numbers and geometric figures and construction techniques.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, B) → u
  3. Point(xAxis) → C
  4. Vector(C, D) → v
  5. Point(xAxis) → E
  6. Vector(E, F) → w
  7. Angle(E, A, B) → α
  8. Angle(E, C, D) → β
  9. Point(xAxis) → z_1
  10. Angle(z_1, E, F) → γ
  11. Sequence(Segment[(0, q), (3, q)], q, 0, 3) → list1
  12. Sequence(Segment[(q, 0), (q, 3)], q, 0, 3) → list2
  13. If(1 ≤ a < 2, Vector[(0, 0), Dilate[(0, 0), 2 - a, (1, 1)]], Vector[(1, 1)]) → b
  14. If(3 ≤ a < 4, Vector[(1, 1), Dilate[(1, 1), 4 - a, (0, 2)]], Vector[(1, 1), (0, 2)]) → c
  15. If(4 ≤ a < 5, Vector[(0, 2), Dilate[(0, 2), 5 - a, (-1, 3)]], Vector[(0, 2), (-1, 3)]) → d
  16. If(6 ≤ a < 7, Vector[(0, 0), Dilate[(0, 0), 7 - a, (-1, 3)]], Vector[(0, 0), (-1, 3)]) → e
  17. If(9 ≤ a < 10, Vector[(-4, 2), Dilate[(-4, 2), 10 - a, (-7, 1)]], Vector[(-4, 2), (-7, 1)]) → g
  18. If(8 ≤ a < 9, Vector[(-1, 3), Dilate[(-1, 3), 9 - a, (-4, 2)]], Vector[(-1, 3), (-4, 2)]) → f
  19. If(10 ≤ a < 11, Vector[(-7, 1), Dilate[(-7, 1), 11 - a, (-10, 0)]], Vector[(-7, 1), (-10, 0)]) → h
  20. If(12 ≤ a < 13, Vector[Dilate[(0, 0), 13 - a, (-10, 0)]], Vector[(-10, 0)]) → i
  21. Angle((1, 0), (0, 0), (1, 1)) → δ
  22. Angle((1, 1), (0, 0), (-1, 3)) → ε
  23. Angle((-1, 3), (0, 0), (-10, 0)) → ζ