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

[raghavendar24]

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

 

[Dale]

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.

 

[raghavendar24]

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.

 

[Dale]

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]

 

[raghavendar24]

Thank you so much.



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

 

[raghavendar24]

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

 

[Dale]

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.

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

 

[raghavendar24]

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

 

[Dale]

Yes, that looks correct.