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Complex Multiplication by kosband

Complex Multiplication by kosband
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2015-03-12 10:56
VectorCoordinate GeometryComplex Number
This example illustrates the process of complex number multiplication. It involves the basic operations and geometric meaning of complex numbers. Using GeoGebra commands such as Intersect, Vector, Circle, etc., it visually demonstrates how complex number multiplication affects points on the complex plane. Suitable for high school mathematics education and learning complex number concepts.

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