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Plot graphs using Mathematica 
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#1
Aug2109, 03:04 AM

P: 9

hi ,
i am unable to draw the graphs of complex valued functions using mathematica, please help me . Ex:koebe function. z/(1z)^2, z is a complex number 


#2
Aug2109, 06:55 AM

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P: 17,322

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.



#3
Aug2109, 07:12 AM

P: 9

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. 


#4
Aug2109, 07:47 PM

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P: 17,322

Plot graphs using Mathematica
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] 


#5
Aug2409, 12:45 AM

P: 9

Thank you so much.
Can you suggest me any book which is useful to plot this type of functions using mathematica 


#6
Aug2409, 03:40 AM

P: 9

Hi one more doubt regarding the above problem,
The function z/(1z)^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 


#7
Aug2409, 11:18 AM

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P: 17,322




#8
Aug2409, 11:32 AM

P: 9

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 


#9
Aug2409, 02:02 PM

Mentor
P: 17,322

Yes, that looks correct.



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