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Geometric Representation of Complex Roots by Juan Carlos Ponce Campuzano

Geometric Representation of Complex Roots by Juan Carlos Ponce Campuzano
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2014-11-18 13:20
TrigonometryComplex NumberGeometric Construction
This example demonstrates the geometric representation of the roots of a complex number in the complex plane. Key math concepts include complex numbers, roots, trigonometric functions, and geometric construction. It utilizes GeoGebra commands and objects such as Point, Angle, Sequence, Textfield, Max, Element, and Circle. Suitable for high school mathematics education and complex number learning.

GeoGebra Commands & Parameters

  1. Point(v) → C
  2. Point(xAxis) → B
  3. Angle(B, C, A) → α
  4. Sequence((r^(1 / n) * cos((α + ((2 * π) * i)) / n)), i, 0, n - 1, 1) → list3, {1.330922910810629, 0.21079748034384427, -1.2006429032152952, -0.9528356028822473, 0.6117581149430692}
  5. Sequence((r^(1 / n) * sin((α + ((2 * π) * i)) / n)), i, 0, n - 1, 1) → list4, {0.2107974803438442, 1.330922910810629, 0.6117581149430694, -0.9528356028822471, -1.2006429032152957}
  6. Sequence(((r^(1 / n) * cos((α + ((2 * π) * i)) / n)), (r^(1 / n) * sin((α + ((2 * π) * i)) / n))), i, 0, n - 1, 1) → list1, {(1.330922910810629, 0.2107974803438442), (0.21079748034384427, 1.330922910810629), (-1.2006429032152952, 0.6117581149430694), (-0.9528356028822473, -0.9528356028822471), (0.6117581149430692, -1.2006429032152957)}
  7. Sequence(Segment[(0, 0), ((r^(1 / n) * cos((α + ((2 * π) * i)) / n)), (r^(1 / n) * sin((α + ((2 * π) * i)) / n)))], i, 0, n - 1, 1) → list2, {1.3475130323080184, 1.3475130323080184, 1.3475130323080182, 1.3475130323080187, 1.3475130323080187}
  8. Textfield(a) → inputBox1
  9. Textfield(b) → inputBox2
  10. Textfield(n) → inputBox3
  11. Max(list6) → c
  12. Max(list5) → d
  13. Element(list1, A1) → B1
  14. Element(list1, A2) → B2
  15. Element(list1, A3) → B3
  16. Element(list1, A4) → B4
  17. Element(list1, A5) → B5
  18. Element(list1, A6) → B6
  19. Element(list1, A7) → B7
  20. Element(list1, A8) → B8
  21. Element(list1, A9) → B9
  22. Element(list1, A10) → B10
  23. Element(list1, A11) → B11
  24. Element(list1, A12) → B12
  25. Element(list1, A13) → B13
  26. Element(list1, A14) → B14
  27. Element(list1, A15) → B15
  28. Element(list1, A16) → B16
  29. Element(list1, A17) → B17
  30. Element(list1, A18) → B18
  31. Element(list1, A19) → B19
  32. Element(list1, A20) → B20
  33. Element(list1, A21) → B21
  34. Element(list1, A22) → B22
  35. Element(list1, A23) → B23
  36. Element(list1, A24) → B24
  37. Element(list1, A25) → B25
  38. Element(list1, A26) → B26
  39. Element(list1, A27) → B27
  40. Element(list1, A28) → B28
  41. Element(list1, A29) → B29
  42. Element(list1, A30) → B30
  43. Element(list1, A31) → B31
  44. Element(list1, A32) → B32
  45. Element(list1, A33) → B33
  46. Element(list1, A34) → B34
  47. Element(list1, A35) → B35
  48. Element(list1, A36) → B36
  49. Element(list1, A37) → B37
  50. Element(list1, A38) → B38
  51. Element(list1, A39) → B39
  52. Element(list1, A40) → B40
  53. Element(list1, A41) → B41
  54. Element(list1, A42) → B42
  55. Element(list1, A43) → B43
  56. Element(list1, A44) → B44
  57. Element(list1, A45) → B45
  58. Element(list1, A46) → B46
  59. Element(list1, A47) → B47
  60. Element(list1, A48) → B48
  61. Element(list1, A49) → B49
  62. Element(list1, A50) → B50
  63. Element(list1, A51) → B51
  64. Circle(C, r^(1 / n)) → e
  65. Max(c, d) → f

AI Drawing Prompt Reference

Draw a geometric representation of the n-th roots of a complex number in the complex plane. The figure includes the origin, a point B on the x-axis, angle α, and n points representing the roots (line segments from the origin). Also add text boxes for input parameters. The construction order is: define points C and B, define angle α; generate the coordinates of the roots; draw line segments from the origin to these points; finally add the text boxes.
The prompt above was compiled from the original drawing commands and is for reference only.