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Complex Roots by kosband

Complex Roots by kosband
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2015-03-19 03:07
FunctionCoordinate GeometryComplex Number
This example illustrates the concept of complex roots. It involves basic knowledge of quadratic functions and complex numbers. Using GeoGebra commands such as Intersect, Sequence, Circle, etc., the complex roots can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Sequence((Z^(1 / n) * exp((((i * 2) * 3.141592653589793) * k / n))), k, 0, n - 1) → Roots
  3. Circle(O, Z) → ZCircle
  4. Vector(O, Z) → ZVector
  5. Circle(O, (abs(ZVector))^(1 / n)) → WCircle
  6. Point(WCircle) → W
  7. Sequence(Text["W^{" + (k) + "}", W^(k), n > 0, n > 0], k, 2, n) → WLabels
  8. Sequence(Vector[O, W^(k)], k, 1, n) → WVectors
  9. Sequence(Text["W_{" + (k) + "}", Element[Roots, k], n > 0, n > 0], k, 1, n) → RootsLabels
  10. Sequence(Vector[O, Element[Roots, k]], k, 1, n) → RootsVectors
  11. Sequence(Circle[O, abs(W^(k))], k, 2, n - 1) → WCircles