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Powers of Complex Numbers

Powers of Complex Numbers
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2020-03-17 05:02
FunctionComplex NumberTransformationSlider AnimationLocus
This example demonstrates the power operation of complex numbers. It shows how the power operation of complex numbers changes on the complex plane. Key mathematical concepts include complex numbers, power operations, and geometric transformations on the complex plane. Using GeoGebra commands such as Locus, Point, and Segment, the trajectory of complex number power operations can be dynamically observed. Suitable for high school mathematics education and learning complex number concepts.

GeoGebra Commands & Parameters

  1. Locus(w, n) → loc1
  2. Textfield(a) → InputBox1
  3. Point(yAxis) → A
  4. Segment(A, a) → g
  5. Segment(A, w) → h
  6. Point(xAxis) → B
  7. Angle(B, A, a) → α
  8. Angle(B, A, w) → β
  9. Rotate(B, 1, A) → B'
  10. Angle(B, A, B') → γ
  11. Rotate(B, (0.5 * β), A) → B'_1
  12. Angle(B, A, B'_1) → δ
  13. Segment(A, B'_1) → j
  14. Point(j) → C
  15. Rotate(B, (0.5 * α), A) → B'_2
  16. Angle(B, A, B'_2) → ε
  17. Segment(A, B'_2) → k
  18. Point(k) → D
  19. Segment(A, a_2) → l
  20. Segment(A, a) → m
  21. Segment(A, a_3) → p
  22. Segment(A, a_4) → q
  23. Segment(A, a_5) → r
  24. Segment(A, a_6) → s
  25. Segment(A, a_7) → t
  26. Segment(A, a_8) → f_1
  27. Segment(A, a_9) → g_1
  28. Segment(A, a_{10}) → h_1
  29. Segment(A, a_{11}) → i_1
  30. Segment(A, a_{12}) → j_1
  31. Segment(A, a_{13}) → k_1
  32. Segment(A, a_{14}) → l_1
  33. Segment(A, a_{15}) → m_1
  34. Segment(A, a_{16}) → n_1
  35. Segment(A, a_{17}) → p_1
  36. Segment(A, a_{18}) → q_1
  37. Segment(A, a_{19}) → r_1
  38. Segment(a_{20}, A) → s_1
  39. Point(loc1) → E
  40. Segment(A, E) → t_1

AI Drawing Prompt Reference

Draw the locus of complex number powers, select point A on the x-axis as the origin, and use slider a to control the power of complex numbers, observing how these powers change on the complex plane. Start by drawing point A, then generate a series of complex numbers using the slider, and use rotation and translation operations to dynamically show their locus. Finally, use the Locus command Locus(w, n) to generate the locus loc1.
The prompt above was compiled from the original drawing commands and is for reference only.