MathPlotAI Logo MathPlotAI

Complex Function Graphing

Complex Function Graphing
Loading the math board and drawing, please wait…
2020-04-16 15:55
FunctionComplex NumberGraphing
This example demonstrates the graphing of complex functions. Key mathematical concepts include complex numbers and their operations. Using GeoGebra commands such as Line, Circle, Mirror, and Intersect, the graph of a complex function can be constructed. Suitable for high school and above students to learn about the properties and graphs of complex functions.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Midpoint(A, B) → C
  3. Circle(C, B) → c
  4. Mirror(D, f) → D'
  5. Mirror(D', c) → D''
  6. Mirror(D, c) → D'_1
  7. Circle(D, D'_1, D') → d
  8. Center(d) → E
  9. Intersect(d, f, 2) → F
  10. Sequence((A + (B * k / n)) / (1 + k / n), k, 1, n) → l1
  11. Sequence((B + (A * k / n)) / (1 + k / n), k, 1, n) → l2
  12. Join({l1, l2}) → liste2
  13. OrthogonalLine(C, f) → g
  14. Intersect(c, g, 2) → G
  15. Midpoint(G, C) → H
  16. Circle(B, H, A) → e
  17. Zip(Circle[P, Mirror[P, e], Mirror[Mirror[P, e], c]], P, liste2) → Liste12
  18. Circle(I, A, B) → h
  19. Mirror(I, e) → I'_1
  20. Mirror(I'_1, f) → z_1
  21. Circle(I, I'_1, z_1) → k
  22. Line(J, K) → i
  23. OrthogonalLine(J, i) → j
  24. Circle(K, J) → p
  25. Point(j) → L
  26. Circle(L, J) → q
  27. Sequence(K + (exp(((k / n * ί) * π)) * (K - J)), k, 0, n - 1) → PListe
  28. Zip(Circle[P, Mirror[P, j], J], P, PListe) → liste6
  29. Zip(Mirror[Circle[P, Mirror[P, j], J], i], P, PListe) → cercles22
  30. Join({liste6, cercles22}) → Liste3
  31. Sequence(L + (ℯ^(((k / n * ί) * π)) * (L - J)), k, 0, n - 1) → liste7
  32. Zip(Circle[P, Mirror[P, i], J], P, liste7) → liste10
  33. Zip(Mirror[Circle[P, Mirror[P, i], J], j], P, liste7) → cercles2
  34. Join({liste10, cercles2}) → Liste4
  35. Mirror(M, j) → M'
  36. Circle(M, M', J) → r
  37. Mirror(M, i) → M'_1
  38. Circle(M, M'_1, J) → s
  39. Sequence(k, k, 1, n) → liste1
  40. Zip((((B - F) * A) - (((A - F) * B) * exp(((k / n * ί) * π)))) / (B - F - ((A - F) * exp(((k / n * ί) * π)))), k, liste1) → HypPteListe
  41. Zip(Circle[A, B, P], P, HypPteListe) → HyperListe