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Complex Multiplication by Martin Flashman

Complex Multiplication by Martin Flashman
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2016-02-24 23:38
AngleFunctionComplex Number
In collections Mapping Diagrams to Visualize Complex Analysis
This example illustrates the process of complex number multiplication. It involves the concepts of argument and modulus of complex numbers. Using GeoGebra commands such as Angle, Segment, and CurveCartesian, the geometric meaning of complex number multiplication is demonstrated. Suitable for high school mathematics education to help students understand complex number multiplication.

GeoGebra Commands & Parameters

  1. Angle(z_4, z_3, z_1) → θ_1
  2. Segment(z_3, z_1) → r_1
  3. Segment(z_3, z_2) → r_2
  4. Segment(z_2, z_{z_1+z_2}) → d
  5. Segment(z_1, z_{z_1+z_2}) → e
  6. Segment(z_3, z_{z_1*z_2}) → r_{z_1*z_2}
  7. Angle(z_4, z_3, z_2) → θ_2
  8. Angle(z_4, z_3, z_{z_1*z_2}) → β
  9. Segment(z_2, z_{z_1*z_2}) → c
  10. CurveCartesian(((1 - t) * x(z_1)) + (t * x(z_{z_1*z_2})), ((1 - t) * y(z_1)) + (t * y(z_{z_1*z_2})), t, 0, 1) → f