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Interactive Complex Numbers & Calculus Example

Interactive Complex Numbers & Calculus Example
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2020-02-15 21:45
CalculusComplex NumberGeometric Construction
This example demonstrates the dynamic relationship between complex numbers and calculus through interactive visualization, focusing on function graphs and complex operations. It involves core concepts like complex numbers, calculus, isosceles triangles, and median value theorem. GeoGebra commands such as Random, RandomElement, Sequence, If, Min, Length, Solutions, Element, TableText, SurdText are utilized in construction. Suitable for high school and above learners to understand the application of complex operations and calculus in geometric problems.

GeoGebra Commands & Parameters

  1. Random(1, 2) → a1
  2. RandomElement({3, 4}) → b
  3. Random(1, 3) → a2
  4. Sequence(x(Element[l2, i]), i, 1, Length[l2]) → l4
  5. Sequence(x(Element[l1, i]), i, 1, Length[l1]) → l3
  6. If(d ≟ 1, l3, l4) → l5
  7. Min(l5) → c1
  8. Sequence(SurdText[x(Element[l1, i]), {sqrt(2), sqrt(3), sqrt(5)}], i, 1, Length[l1]) → l6
  9. Sequence(SurdText[x(Element[l2, i]), {sqrt(2), sqrt(3), sqrt(5)}], i, 1, Length[l2]) → l7
  10. If(d ≟ 1, l6, l7) → l8
  11. Length(l8) → e
  12. Solutions(h = h1) → l10
  13. Solutions(h(x) > l) → l9
  14. Element(l9, 1) → i
  15. If(d ≟ 1, "real", "imaginary") → text4
  16. Length(l5) → a
  17. If(a ≟ 4, Element[l5, 2], 0) → c2
  18. Sequence(a1 + ((a2 * Element[l5, i]) * ί), i, 1, a) → l11
  19. Sequence(SurdText[Element[l11, i]], i, 1, a) → l12
  20. TableText(l8, "c") → text7
  21. TableText(l12, "c") → text2
  22. Sequence(Sequence[Element[l8, j], i, 1, 1], j, 1, e) → l13
  23. TableText(l13, "c{") → text8
  24. Sequence(Sequence[Element[l12, j], i, 1, 1], j, 1, e) → l14
  25. TableText(l14, "c{") → text9
  26. SurdText(arg(z1^(j)), {π}) → α
  27. SurdText(k, {sqrt(2), sqrt(3)}) → text11
  28. RandomElement({3, 4}) → b_1