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Roots of Complex Numbers Visualization

Roots of Complex Numbers Visualization
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2017-04-19 23:08
FunctionComplex NumberGeometric Construction
This example demonstrates how to visualize the roots of complex numbers in the complex plane. It involves core mathematical concepts such as complex numbers, roots, derivatives, logarithmic functions, planes, special points, and functions. The construction utilizes GeoGebra commands like Angle, Length, Intersect, Vector, Point, Distance, and Midpoint. Suitable for high school and above mathematics education to understand complex operations and geometric representations.

GeoGebra Commands & Parameters

  1. Angle(z) → α
  2. Length(z) → a
  3. Intersect(xAxis, yAxis) → A
  4. Vector(A, z) → u
  5. Vector(A, z_0) → v
  6. Vector(A, z_1) → w
  7. Vector(A, z_2) → b
  8. Vector(A, z_3) → c
  9. Vector(A, z_4) → d
  10. Vector(A, z_5) → e
  11. Vector(A, z_6) → f
  12. Vector(A, z_7) → g
  13. Vector(A, z_8) → h
  14. Point(xAxis) → B
  15. Angle(B, A, z) → β
  16. Angle(B, A, z_0) → γ
  17. Angle(B, A, z_1) → δ
  18. Angle(B, A, z_1) → ε
  19. Distance(A, z_0) → distanceAz0
  20. Midpoint(A, z_0) →
  21. Distance(A, z_1) → distanceAz1
  22. Midpoint(A, z_1) →
  23. Angle(B, A, z_0) → ζ
  24. Angle(B, A, z_1) → η
  25. Angle(B, A, z_2) → θ
  26. Distance(A, z_2) → distanceAz2
  27. Midpoint(A, z_2) →
  28. Distance(A, z) → distanceAz
  29. Midpoint(A, z) →