Mathematica How can Mathematica be used to plot graphs of complex valued functions?

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Mathematica can be used to plot complex-valued functions like the Koebe function, z/(1-z)^2, through techniques such as ContourPlot and ParametricPlot. Users can visualize the absolute value and argument of the function to represent contours and colors effectively. Specific code examples provided include ParametricPlot for the function and Plot3D to illustrate its mapping. The discussion also touches on how this function maps the unit disk onto the entire plane, excluding a line segment from negative infinity to -1/4. For further learning, online help and suggested books on Mathematica are recommended for plotting complex functions.
raghavendar24
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hi ,


i am unable to draw the graphs of complex valued functions using mathematica,

please help me .

Ex:koebe function. z/(1-z)^2, z is a complex number
 
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How do you want to display the function? One common approach is to use ContourPlot and plot the Abs as the contours and use Arg for the colors.
 
Hi, thnx for reply, please say how to plot in two ways so that i can use which is is required for me, and other one i may use whenever i needed.

Thank you.
 
ParametricPlot[
Through[{Re, Im}[(x + I y)/(1 - (x + I y))^2]], {x, 0, 2}, {y, -1,
1}, PlotRange -> {-1, 1}]


Plot3D[Abs[(x + I y)/(1 - (x + I y))^2], {x, 0, 2}, {y, -1, 1},
ColorFunction ->
Function[{x, y},
Hue[Arg[(x + I y)/(1 - (x + I y))^2]/(2 \[Pi]) + .5]],
ColorFunctionScaling -> False]
 
Thank you so much.



Can you suggest me any book which is useful to plot this type of functions using mathematica
 
Hi one more doubt regarding the above problem,

The function z/(1-z)^2 maps the unit disk |z|<1 onto the entire plane except a line segment

from (-infinity to -1/4) , how can we show that using the above function plot using mathematica.

Thanking you
 
raghavendar24 said:
Can you suggest me any book which is useful to plot this type of functions using mathematica
I have found the online help (F1) to be quite thorough.

raghavendar24 said:
Hi one more doubt regarding the above problem,

The function z/(1-z)^2 maps the unit disk |z|<1 onto the entire plane except a line segment

from (-infinity to -1/4) , how can we show that using the above function plot using mathematica.
Use the parametric plot version shown above, but map the complex plane using r Exp[-I theta] instead of x + I y
 
I already work out at that time i have some doubt whether it is right or not, thank you now i conformed but here is a problem i m unable to interpret from the figure it mapping the unit disk

that is |z|<1 (in polar form we are using r Exp(I*theta)


r varies from 0 to 1

and theta varies from 0 to 2 pi )


to the entire XY plane except a line segment
 

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Yes, that looks correct.
 
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