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Ratio of Two Complex Numbers

Ratio of Two Complex Numbers
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2016-04-13 19:20
VectorComplex NumberGeometric Construction
In collections complex numbers
This example demonstrates the geometric representation of the ratio of two complex numbers in the complex plane. Key math concepts include complex numbers, modulus, argument, and complex conjugate. It is constructed using GeoGebra commands like Intersect, Vector, Length, and Angle, involving objects such as z_1, z_2, and their ratio components. Suitable for high school and above learners exploring the geometric interpretation of complex operations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Vector(A, z_1) → u
  3. Vector(A, z_2) → v
  4. Vector(A, z_3) → w
  5. Vector(A, z_4) → z
  6. Vector(A, z_5) → c
  7. Length(z_3) → e
  8. Length(z) → lengthofproduct
  9. Length(c) → lengthofratio
  10. Length(z_1) → lengthofz1
  11. Length(z_2) → lengthofz2
  12. Angle(u) → α
  13. Angle(v) → β