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Mapping Diagrams in Complex Analysis

Mapping Diagrams in Complex Analysis
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2017-05-29 09:04
FunctionComplex NumberGeometric ConstructionLocusGraphing
In collections Mapping Diagrams to Visualize Complex Analysis
This example demonstrates mapping diagrams for complex functions and continuity. It involves core concepts like complex numbers, function mapping, and continuity. Constructed using GeoGebra commands and objects such as Textfield, Expand, Sequence, Zip, Circle, Line, Vector, Point, and Locus. Suitable for university mathematics students and learners of complex analysis.

GeoGebra Commands & Parameters

  1. Textfield(G) → InputBox1
  2. Expand(Simplify[G(x + (y * ί), 0, x(a_#) + (y(a_#) * ί), 0, x(b_#) + (y(b_#) * ί), 0)]) → Gz
  3. Expand(Simplify[H(x + (y * ί), 0, x(a_#) + (y(a_#) * ί), 0, x(b_#) + (y(b_#) * ί), 0, x(c_#) + (y(c_#) * ί), 0, x(d_#) + (y(d_#) * ί), 0)]) → Hz
  4. Textfield(H) → InputBox2
  5. Sequence(0, m) → M
  6. Zip(((2 * π) * k / m), k, M) → t_*
  7. Zip((δ * ℯ^((t * ί))) + z_#, t, t_*) → z_*
  8. Circle(z_#, δ) → c
  9. Zip(Hr(x(z), y(z)) + (Hi(x(z), y(z)) * ί), z, z_*) → hz_*
  10. Zip(Gr(x(z), y(z)) + (Gi(x(z), y(z)) * ί), z, z_*) → gz_*
  11. Zip((x(z), y(z), ht), z, hz_*) → hpt_*
  12. Zip((x(z), y(z), ht), z, gz_*) → gpt_*
  13. Line(O, ZY1) → Yax
  14. Line(O, ZX1) → Xax
  15. Zip(Vector[A, B], A, z_*, B, gpt_*) → gvec_*
  16. Zip(Vector[A, B], A, z_*, B, hpt_*) → hvec1_*
  17. Vector(z_#, Gz1_#) → vecg_#
  18. Vector(z_#, Hz1_#) → vech_#
  19. Point(c) → A
  20. Locus(PtAG, A) → gLoc
  21. Locus(PtAH, A) → hLoc
  22. Circle(Gz1_#, ε_g, xOyPlane) → cε_g
  23. Circle(Hz1_#, ε_h, xOyPlane) → cε_h