Powers of Complex Numbers by Judah L Schwartz (4)

Powers of Complex Numbers by Judah L Schwartz (4)
Loading the math board and drawing, please wait…
2017-03-22 05:34
This example demonstrates the geometric representation of powers of complex numbers, showing the effect of multiplication through rotation and scaling. It involves core mathematical concepts such as the polar form of complex numbers, Euler's formula, and rotational and scaling transformations. Constructed using GeoGebra commands like Intersect, Circle, Rotate, Angle, ToComplex, ToPolar, Vector, Mirror, it provides a visual and dynamic illustration of complex operations. Suitable for high school and above, helping learners understand the geometric meaning of complex operations and deepen their understanding of complex number properties.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Rotate(C, (360 / N)°, A) → Nroot
  4. Angle(C, A, Nroot) → α_1
  5. ToComplex(Vector[Nroot]) → u
  6. ToPolar(Vector[Nroot]) → v
  7. Vector(NrootPower) → w
  8. ToPolar(w) → z
  9. Angle(C, A, NrootPower) → β
  10. ToComplex(w) → a
  11. ToComplex(Vector[Z]) → CZ
  12. Mirror(Z, xAxis) → ZC
  13. Mirror(ZC, c) → ZCI
  14. ToComplex(Vector[ZC]) → CZC
  15. ToComplex(Vector[ZCI]) → CZCI
  16. Vector(Zpower) → h
  17. Vector(z_1) → j
  18. Vector(z_2) → k
  19. Vector(z_3show) → l
  20. Vector(z_2show) → m
  21. Mirror(Z, c) → ZRI