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Geometric Interpretation of Complex Number Multiplication by Victor Hui

Geometric Interpretation of Complex Number Multiplication by Victor Hui
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2011-12-18 01:02
VectorComplex NumberGeometric Construction
In collections Complex numbers
This example geometrically demonstrates the multiplication of complex numbers, showing how multiplication corresponds to rotation and scaling of vectors in the complex plane. Key math concepts include complex numbers, vectors, rotation, scaling, and geometric transformations. GeoGebra commands used in construction are Intersect, Vector, Circle, Polygon, and Dilate. Suitable for high school and above students to understand the visual essence of complex operations and for teaching the connection between complex numbers and geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Vector(O, W) → Wvec
  3. Vector(O, Z) → Zvec
  4. Vector(O, Q) → Qvec
  5. Circle(O, Z) → z
  6. Circle(O, W) → w
  7. Polygon(W, O, U) → WOU, ZO, OU, UZ
  8. Polygon(Q, O, Z) → QOZ, QO, OW, WQ
  9. Dilate(Rotate[Z, -r * Angle[Z], O], 1 + s * (abs(W) / abs(Q) - 1), O) → Z'
  10. Dilate(Rotate[Q, -r * Angle[Z], O], 1 + s * (abs(W) / abs(Q) - 1), O) → Q'
  11. Polygon(Q', O, Z') → QOZ', QO', OW', WQ'
  12. Circle(O, Q) → q