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Nth Roots of a Complex Number by Anna-Lena Boch

Nth Roots of a Complex Number by Anna-Lena Boch
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2018-11-19 22:00
AngleSequenceComplex Number
This example demonstrates the nth roots of a complex number. By adjusting parameters, you can observe how the roots change with different n values. Key mathematical concepts include complex numbers, the concept of roots, and calculations of angles and moduli. GeoGebra commands used include Length, Sequence, Segment, Angle, etc. Suitable for high school mathematics education and learning.

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