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Complex Function Mapping Diagrams and Real Cubic Equations

Complex Function Mapping Diagrams and Real Cubic Equations
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2017-07-06 09:31
FunctionCalculusComplex Number
In collections Mapping Diagrams to Visualize Complex Analysis
This example illustrates complex function mapping and solving real cubic equations. Key mathematical concepts include complex numbers, function mapping, and the roots of cubic equations. Using GeoGebra commands such as ComplexRoot, Sequence, and Zip, the geometric meaning of complex roots is dynamically demonstrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. ComplexRoot(f) → r_1, r_2, r_3
  2. Sequence((δ * (cos(t) + (sin(t) * ί))) + real(z_#) + (imaginary(z_#) * ί), t, -3.14159, π, (2 * π / m)) → z_*
  3. Zip(f_C[z, p, q], z, z_*) → fz_*
  4. f_C(z_#, p, q) → f_{(z#)}
  5. Sequence((x(Element[fz_*, k]), y(Element[fz_*, k]), height_{image}), k, 1, m) → fpoint_*
  6. Vector(z_#, f_{(z#).}) → w
  7. CurveCartesian(t, 0, height_{image}, t, -5, 5) → Xh
  8. CurveCartesian(0, t, height_{image}, t, -5, 5) → Yh
  9. PointIn(C_{image}) → L
  10. Sequence(Vector[Element[z_*, j], Element[fpoint_*, j]], j, 1, m) → fvec_*
  11. Intersect(f, xAxis) → A, B, C
  12. Zip(Vector[(x(z), y(z), 0), (0, 0, height_{image})], z, roots) → rootsvec
  13. Circle(r_3, r_2, r_1) → c
  14. Center(c) → O_r
  15. Point(circle) → P_C
  16. Locus(F_D, P_C) → f_{circ}
  17. Radius(c) → δ_r
  18. Textfield(p) → InputBox1
  19. Textfield(q) → InputBox2