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Nth Roots of a Complex Number by Anna-Lena Boch (2)

Nth Roots of a Complex Number by Anna-Lena Boch (2)
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2018-11-19 21:59
TrigonometrySequenceComplex NumberGeometric Construction
This example demonstrates how to plot all nth roots of a complex number on the complex plane. It involves core mathematical concepts such as the modulus and argument of a complex number, polar coordinates, trigonometric functions, and sequences. The construction uses GeoGebra commands/objects like Length, Sequence, Segment, Angle, and Element. Suitable for high school and above mathematics learners to understand complex number operations and geometric representations.

GeoGebra Commands & Parameters

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