# Plot graphs using Mathematica

• Mathematica
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

## Answers and Replies

Dale
Mentor
2020 Award
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.

Dale
Mentor
2020 Award
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

Dale
Mentor
2020 Award
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

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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Dale
Mentor
2020 Award
Yes, that looks correct.