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Mapping Diagrams for Complex Quadratic Functions & Equations

Mapping Diagrams for Complex Quadratic Functions & Equations
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2018-01-20 03:16
FunctionCoordinate GeometryComplex NumberLocusGraphing
In collections Mapping Diagrams to Visualize Complex Analysis
This example demonstrates mapping diagrams for complex quadratic functions and equations, visually illustrating the function's graph and mapping relationships. Key math concepts include complex numbers, function mapping, coordinate geometry, and analytical geometry. Construction highlights involve GeoGebra commands like Sequence, Zip, Line, Circle, Point, If, Vector, Textfield, and Locus. Suitable for high school and above students to understand the geometric meaning and properties of complex functions.

GeoGebra Commands & Parameters

  1. Sequence(0, n) → M_1
  2. Zip(((2 * pi) * k / n), k, M_1) → t_*
  3. Zip((δ * ℯ^((t * ί))) + z_#, t, t_*) → z_c
  4. Zip(z_# + ((t - pi) * (P_l - z_#)), t, t_*) → z_l
  5. Line(z_#, P_l) → l
  6. Circle(z_#, δ) → c
  7. Point(c) → Pc
  8. If(m ≟ 1, z_c, z_l) → z_*
  9. Zip(s1(z), z, z_*) → fz_*
  10. Line(O, ZY1) → Im_{axis}
  11. Line(O, ZX1) → Real_{axis}
  12. Vector(z_#, fz1_#) → vecf_#
  13. Textfield(F) → InputBox1
  14. Zip((x(z), y(z), ht), z, fz_*) → fpt_*
  15. Zip(Vector[z, w], z, z_*, w, fpt_*) → fvec_*
  16. Locus(Pts1Pc, Pc) → loc_c
  17. Point(l) → Pl
  18. Locus(Pts1Pl, Pl) → loc_l
  19. Line((x(O2), y(O2), z(O2)), Vector[(1, 0, 0)]) → Real_{axis2}
  20. Line((x(O2), y(O2), z(O2)), Vector[(0, 1, 0)]) → Im_{axis2}
  21. Zip(g(s1(z)), z, z_*) → gfz_*
  22. Zip((x(z), y(z), (2 * ht)), z, gfz_*) → gfpt_*
  23. Zip(Vector[z, w], z, fpt_*, w, gfpt_*) → gfvec_*
  24. Locus(Ptgs1Pc, Pc) → loc2_c
  25. Textfield(G) → InputBox2
  26. Sequence(n_p) → Np
  27. Zip(z = (ht * k), k, Np) → Planes
  28. Zip(mf(g(s1(z))), z, z_*) → Agfz_*
  29. Zip((x(z), y(z), (3 * ht)), z, Agfz_*) → Agfpt_*
  30. Zip(Vector[z, w], z, gfpt_*, w, Agfpt_*) → Agfvec_*
  31. Zip(s2(mf(SQ(s1(z)))), z, z_*) → kAgfz_*
  32. Zip((x(z), y(z), (4 * ht)), z, kAgfz_*) → kAgfpt_*
  33. Zip(Vector[z, w], z, Agfpt_*, w, kAgfpt_*) → kAgfvec_*
  34. Locus(PtAgs1Pc, Pc) → Loc3_c
  35. Locus(Pts2Ags1Pc, Pc) → Loc4_c
  36. Locus(Ptgs1Pl, Pl) → loc2_l
  37. Locus(PtAgs1Pl, Pl) → Loc3_l
  38. Locus(Pts2Ags1Pl, Pl) → Loc4_l
  39. Vector(B3, Is2B3) → u
  40. Vector(Is2B3, IAIs2B3) → v
  41. Vector(IAIs2B3, SQRPIAIs2B3) → w
  42. Vector(IAIs2B3, SQRNIAIs2B3) → b
  43. Vector(SQRPIAIs2B3, Is1SQRPIAIs2B) → e
  44. Vector(SQRNIAIs2B3, Is1SQRNIAIs2B) → d