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Roots of Unity by James R Olsen

Roots of Unity by James R Olsen
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2018-03-06 00:05
TrigonometrySequenceComplex Number
This example demonstrates the concept of roots of unity, which are the nth roots of unity on the unit circle in the complex plane, involving complex numbers and trigonometry. Using GeoGebra commands such as Sequence, Segment, and Angle, the construction of the roots of unity is dynamically illustrated. Suitable for high school mathematics education, particularly in the study of complex numbers and trigonometry.

GeoGebra Commands & Parameters

  1. Sequence(cos(((2 * k) * π / n)) + (ί * sin(((2 * k) * π / n))), k, 0, n - 1) → list1
  2. Sequence(Segment[Element[list1, k], Element[list1, k + 1]], k, 1, n - 1) → list2
  3. Segment(Element[list1, n], Element[list1, 1]) → a
  4. Sequence(Segment[(0, 0), Element[list1, j]], j, 1, n) → list3
  5. Angle(Element[list3, 1], Element[list3, 2]) → α
  6. Element(list1, A1) → B1
  7. Element(list1, A2) → B2
  8. Element(list1, A3) → B3
  9. Element(list1, A4) → B4
  10. Element(list1, A5) → B5
  11. Element(list1, A6) → B6
  12. Element(list1, A7) → B7
  13. Element(list1, A8) → B8
  14. Element(list1, A9) → B9
  15. Element(list1, A10) → B10
  16. Element(list1, A11) → B11
  17. Element(list1, A12) → B12
  18. Element(list1, A13) → B13
  19. Element(list1, A14) → B14
  20. Element(list1, A15) → B15
  21. Element(list1, A16) → B16
  22. Element(list1, A17) → B17
  23. Element(list1, A18) → B18
  24. Element(list1, A19) → B19
  25. Element(list1, A20) → B20