# Plotting a complex function under transformation

I am trying to plot the unit circle $$\vert z\vert=1$$ under the transformation $$z\to z+\frac1z$$ using mathematica. In general I want to plot a complex function $$f(z)$$ under the transformation $$\phi(z)$$.

I tried

With[{z=x+I y}, ContourPlot[Norm[z+1/z]==1, {x,-0.75,0.75},{y,-3,3}]]


Which does not seem to produce the correct output

• This was a popular question mathematica.stackexchange.com/questions/156339/… – yarchik Feb 14 at 19:43
• Your code produces points z on the complex plane such that the absolute value of z+1/z is equal to 1 and so it is a different than the transformation of the uinit circle under mapping z+1/z. This answer provides almost the same what you want Plotting complex numbers as an Argand Diagram. First read and then it becomes clear. – Artes Feb 14 at 19:55