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Nth Roots of Complex Numbers by yj3chun

Nth Roots of Complex Numbers by yj3chun
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2017-10-21 20:07
VectorComplex NumberGeometric Construction
This example demonstrates the geometric distribution of nth roots of complex numbers in the complex plane. It involves core mathematical concepts like polar form of complex numbers, nth root formula, and principal argument. Construction uses commands/objects such as Length, Intersect, Point, Sequence, Vector, Circle, and Angle. Suitable for high school and above mathematics learners to understand complex operations and geometric intuition.

GeoGebra Commands & Parameters

  1. Length(z) → r
  2. Intersect(xAxis, yAxis) → O
  3. Point(yAxis) → i
  4. Sequence((z^(1 / n) * ℯ^((((i * 2) * π) * k / n))), k, 0, n - 1) → nthRoots
  5. Vector(O, z) → zvector
  6. Circle(O, Length[z]^(1 / n)) → nthrootcircle
  7. Sequence(Vector[O, Element[nthRoots, k]], k, 1, n) → nthRootsVectors
  8. Angle(z) → argZDegrees
  9. Sequence(Text["w_{" + (k) + "}", Element[nthRoots, k], n > 0, n > 0], k, 1, n) → nthrootnames