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Mapping Diagrams: Complex Analysis-functions with lines or circles

Mapping Diagrams: Complex Analysis-functions with lines or circles
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2017-05-29 08:45
FunctionComplex NumberGeometric ConstructionLocusGraphing
This example demonstrates how complex functions map input complex numbers to output lines or circles. Key math concepts include complex numbers, mapping, and geometric representation. Construction involves GeoGebra commands like Point, Sequence, Zip, Circle, Line, Vector, Locus. Suitable for high school students and beginners in complex analysis learning function properties and visualization.

GeoGebra Commands & Parameters

  1. Point(Line_m) → A_l
  2. Sequence(0, n) → M
  3. Zip(((2 * π) * k / n), k, M) → t_*
  4. Zip(((m * (t - π)) * ί) + t - π + z_#, t, t_*) → z_l
  5. Zip((δ * ℯ^((t * ί))) + z_#, t, t_*) → z_c
  6. Circle(z_#, δ) → circ
  7. Point(circ) → A_c
  8. If(L1orC2 ≟ 2, z_c, z_l) → z_*
  9. Zip(h(z), z, z_*) → hz_*
  10. Zip((x(z), y(z), ht), z, hz_*) → hpt_*
  11. Line(O, ZY1) → Yax
  12. Line(O, ZX1) → Xax
  13. Zip(Vector[A, B], A, z_*, B, hpt_*) → hvec1_*
  14. Vector(z_#, Gz1_#) → vecg_#
  15. Vector(z_#, Hz1_#) → vech_#
  16. If(L1orC2 ≟ 2, x(A_c) + (y(A_c) * ί), x(A_l) + (y(A_l) * ί)) → A
  17. Textfield(G) → InputBox1
  18. Textfield(H) → InputBox2
  19. Zip(g(z), z, z_*) → gz_*
  20. Zip((x(z), y(z), ht), z, gz_*) → gpt_*
  21. Zip(Vector[A, B], A, z_*, B, gpt_*) → gvec1_*
  22. Point(xAxis) → x_#
  23. Locus(gx_#, x_#) → greal
  24. Locus(hx_#, x_#) → hreal
  25. If(L1orC2 ≟ 2, Locus[PtAG, A_c], Locus[PtAG, A_l]) → gLoc
  26. If(L1orC2 ≟ 2, Locus[PtAH, A_c], Locus[PtAH, A_l]) → hLoc