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Geometric Interpretation of Complex Number Multiplication by Nikky Vanderhout

Geometric Interpretation of Complex Number Multiplication by Nikky Vanderhout
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2014-01-07 12:44
VectorComplex NumberTransformation
In collections Complex Numbers as Vectors
This applet geometrically demonstrates the principle of complex number multiplication. It involves the vector representation of complex numbers and rotation transformations. By constructing vectors, rotations, and intersections, it intuitively shows the effect of complex number multiplication. Suitable for middle school and above students to learn the geometric meaning of complex numbers.

GeoGebra Commands & Parameters

  1. Vector(O, P) → z_1
  2. Vector(O, Q) → z_2
  3. Segment(P, A) → a
  4. Segment(A, O) → b
  5. Angle(A, O, P) → α
  6. Rotate(Q, α, O) → Q'
  7. Angle(Q', O, Q) → β_1
  8. Angle(O, A, P) → β
  9. Rotate(O, (-β), Q) → O'
  10. Angle(O', Q, O) → γ
  11. Ray(Q, O') → c
  12. Ray(O, Q') → d
  13. Intersect(d, c) → R
  14. Segment(Q, R) → e
  15. Segment(R, O) → f
  16. Circle(O, 0.3) → g
  17. Midpoint(R, Q) → B
  18. Segment(O, B) → h
  19. Intersect(g, h) → C,
  20. Rotate(Q, (-α), O) → Q'_1
  21. Rotate(O, (-β), Q) → O'_1
  22. Line(O, Q'_1) → i
  23. Rotate(O, β, Q) → O'_2
  24. Line(Q, O'_2) → j
  25. Intersect(j, i) → D
  26. Segment(Q, D) → k
  27. Segment(D, O) → l
  28. Angle(O, Q, D) → δ
  29. Angle(D, O, Q) → ε
  30. Midpoint(Q, D) → E
  31. Segment(O, E) → m
  32. Intersect(g, m) → F,
  33. Circle(Q, 0.3) → p
  34. Midpoint(O, D) → G
  35. Segment(Q, G) → n
  36. Intersect(p, n) → H,
  37. Vector(O, R) → u
  38. Vector(O, D) → v