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Complex Sine Mapping

Complex Sine Mapping
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2013-11-21 02:18
FunctionTrigonometryComplex Number
This example illustrates how the complex sine maps a stripe in the complex plane into the entire complex plane. Key mathematical concepts include complex numbers and trigonometric functions. Using GeoGebra commands such as Segment, Point, and Locus, the mapping effect of the complex sine can be constructed. Suitable for high school mathematics education and learning about transformations of complex numbers and trigonometric functions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → b
  2. Point(b) → C
  3. Locus(E, C) → loc1
  4. Line(D, F) → c
  5. Point(c) → G
  6. Locus(H, G) → loc2
  7. OrthogonalLine(A, b) → d
  8. Point(d) → I
  9. Locus(J, I) → loc3
  10. OrthogonalLine(B, b) → e
  11. Point(e) → K
  12. Locus(L, K) → loc4
  13. Point(b) → O
  14. Circle(C, O) → k
  15. Point(c) → P
  16. Point(c) → Q
  17. Point(b) → R
  18. Point(b) → S
  19. OrthogonalLine(Q, c) → i
  20. OrthogonalLine(R, c) → j
  21. OrthogonalLine(P, c) → l
  22. OrthogonalLine(R, b) → m
  23. OrthogonalLine(S, b) → p
  24. Intersect(m, l) → T
  25. Intersect(p, l) → U
  26. Intersect(i, p) → V
  27. Intersect(m, i) → W
  28. Polygon(W, V, U, T) → poly1, w, v, u, t
  29. Point(u) → Z
  30. Locus(A_1, Z) → loc5
  31. Point(w) → B_1
  32. Locus(C_1, B_1) → loc6
  33. Point(t) → D_1
  34. Locus(E_1, D_1) → loc7
  35. Point(v) → F_1
  36. Locus(G_1, F_1) → loc8
  37. Point(k) → H_1
  38. Locus(I_1, H_1) → loc9
  39. Vector(J_1, K_1) → z
  40. Vector(K_1, J_1) → n

AI Drawing Prompt Reference

Draw a strip in the complex plane and map it to the entire complex plane using the complex sine function. First, draw a line segment AB, then take a point C on this segment and construct the trajectory of the complex sine function through C. Next, draw a line c perpendicular to AB and take a point G on c, then construct the trajectory of G. Continue by drawing lines d and e perpendicular to c and taking points I and K on d and e, respectively, and construct the trajectories of I and K. Then, draw a circle k with C as its center and take points P, Q, R, and S on c, and construct the trajectories of P, Q, R, and S. Next, draw perpendicular lines from P, Q, R, and S and find the intersections W, V, U, and T of these lines, then connect W, V, U, and T to form a quadrilateral. Finally, construct the mapping trajectories through these points.
The prompt above was compiled from the original drawing commands and is for reference only.