Complex Roots. Graphical interpretation and visualizing.

Roman Chijner, 30/01/2022

Graphical interpretation the Complex Roots: the intersection of implicit functions, which are the zeroed real and imaginary parts of the complex function f(z), respectively: real(f(z))=0 and imaginary(f(z))=0.


  • 1. Exploring a Conformal Mapping.
  • 2. Exploring a Conformal Mapping: f(z)=2π / sqrt(9.82) z⁰·⁵
  • 3. Graphical interpretation and visualizing the complex roots of polynomial functions with Real Coefficients.
  • 4. Graphical interpretation and visualizing the roots of complex function(Cubic): f(z)= a z³+ b z² + c z + d . Coefficients a, b, c and d are Complex numbers.
  • 5. Graphical interpretation and visualizing the complex roots of a function(Quartic): f(z)= a z⁴+ b z³ + c z²+ d z+e. Coefficients a, b, c, d and e are Complex numbers.
  • 6. Graphical interpretation and visualizing the Complex Roots of Transcendental functions with Real Coefficients.
  • 7. Graphical interpretation and visualizing the Complex Roots of Transcendental functions with Real Coefficients.
  • 8. Graphical interpretation and visualizing the Complex Roots of Transcendental functions with Real Coefficients.
  • 9. Graphical interpretation and visualizing the Complex Roots of Transcendental functions with Real Coefficients (New version). 1
  • 10. Graphical interpretation and visualizing the Complex Roots of Transcendental functions with Real Coefficients (New version). 2
  • 11. Points on the Complex Grid
  • 12. 5th root, median curve (that's what I'm calling it)
  • 13. Riemann Hypothesis. This is why it is true (2).
  • 14. Schwarz-Transformation
  • 15. Mappings of the circle to the upper/lower half plane
  • 16. Complex mappings
  • 17. The function f(z)=1/z (Part 2)
  • 18. Taylor Expansion
  • 19. Komplexe Transformation eines Gitters
  • 20. Dreiecksfläche mit komplexen Ecken
  • 21. Abaque de Smith
  • 22. Conformal mapping
  • 23. Conformal mapping rectangular grid
  • 24. Boy-Fläche mit Bryant-Kusner-Parametrisierung
  • 25. Plot contours of the modulus of complex functions
  • 26. Conformal mapping: Visualization
  • 27. Isomorphie: z=exp(ix) und R(x)- Drehmatrizen

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Exploring a Conformal Mapping.

This applet for the function f(z)=1/z considers two cases of conformal mapping. Here you can explore [br] - the origin of its conformal mapping. It is a mapping for a rectangular grid.[br] - case of a movable regular n-gon and its image under a conformal mapping f.
[b]A rectangular grid and its image under a conformal map f(z)=1/z. [/b]
– Roman Chijner

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