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Complex logarithm map (principal branch)

Complex logarithm map (principal branch)
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2017-03-02 08:05
FunctionComplex NumberGraphing
This example demonstrates the graph and properties of the complex logarithm map (principal branch). Key math concepts include complex numbers, logarithmic functions, and branch cuts. Construction highlights involve commands like Polygon, Point, Locus, and Sequence in GeoGebra. Suitable for high school and above students to understand the geometric meaning and branch characteristics of complex functions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → regionA, a, b, c, d
  2. Polygon(E, F, G, H) → regionB, e, f, g, h
  3. Polygon(I, J, K, L) → regionC, i, j, k, l
  4. Point(regionA) → z_1
  5. Locus(w_1, z_1) → fA
  6. Point(regionB) → z_2
  7. Point(regionC) → z_3
  8. Locus(w_2, z_2) → fB
  9. Locus(w_3, z_3) → fC
  10. Sequence(Line[(log(i / 100), 0), (log(i / 100), 1)], i, 1, 100) → GridXn
  11. Sequence(Text["ln(" + (i) + ")", (log(i) - 0.1, -0.2)], i, 1, 1000) → AxisXlog
  12. Sequence(Line[(0, (i * π / 6)), (1, (i * π / 6))], i, -5, 6) → GridY
  13. Sequence(Line[(0, (i * π / 6)), (1, (i * π / 6))], i, 7, 20) → GridYup
  14. Sequence(Line[(0, (i * π / 6)), (1, (i * π / 6))], i, -20, -6) → GridYdown
  15. Sequence(Segment[(log(i), (-π)), (log(i), π)], i, 1, 1000) → GridXp
  16. Sequence(Ray[(log(i), π), (log(i), (100 * π))], i, 1, 1000) → GridXpup
  17. Sequence(Ray[(log(i), (-π)), (log(i), (-100 * π))], i, 1, 1000) → GridXpdown