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Complex Roots by Juan Carlos Ponce Campuzano

Complex Roots by Juan Carlos Ponce Campuzano
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2017-02-28 09:22
AngleComplex NumberTransformation
This example demonstrates the roots of complex numbers. It involves fundamental concepts of complex numbers such as modulus and argument. Using GeoGebra commands like Sequence, TableText, and Angle, the construction of complex roots is illustrated. Suitable for high school mathematics education, particularly in complex numbers and geometric transformations.

GeoGebra Commands & Parameters

  1. Angle((1000, 0), (0, 0), Z) → angleZ
  2. Sequence((rZ^(1 / n) * (cos(thetaZ / n + (((2 * k) * π)) / n) + (ί * sin(thetaZ / n + (((2 * k) * π)) / n)))), k, 0, n - 1) → list1
  3. Sequence({Element[list1, i]}, i, 3, n) → list3
  4. Sequence({Element[list1, i]}, i, 1, n) → list2
  5. TableText(list3) → text1
  6. Segment((0, 0), Z) → g
  7. TableText({{LaTeX[xmax, true, true]}, {LaTeX[xmin, true, true]}, {LaTeX[ymax, true, true]}, {LaTeX[ymin, true, true]}}) → text3
  8. Circle((0, 0), 1) → c
  9. If(0 ≤ (Angle * π) < (2 * π), Angle[(1000, 0), (0, 0), Element[list1, 1]], If[(2 * π) ≤ (Angle * π) < (4 * π), Angle[(1000, 0), (0, 0), Element[list1, 2]], Angle[(1000, 0), (0, 0), Element[list1, 3]]]) → α
  10. If(0 ≤ (Angle * π) < (2 * π), Segment[(0, 0), Element[list1, 1]], If[(2 * π) ≤ (Angle * π) < (4 * π), Segment[(0, 0), Element[list1, 2]], Segment[(0, 0), Element[list1, 3]]]) → f
  11. Textfield(Angle) → InputBox1
  12. Textfield(Modulus) → InputBox2
  13. Textfield(user1x) → InputBox3
  14. Textfield(user1y) → InputBox4
  15. Textfield(user2x) → InputBox5
  16. Textfield(user2y) → InputBox6
  17. Element(list1, 1) → z_1
  18. Element(list1, 2) → z_2