(All images created with MATLAB® software)
Click on pictures for more information and an image of higher resolution.
To construct the Riemann Surface for the function f(z)=log((z+1)/(z-1)), we start with the complex plane with a single cut on the real axis (from x = -1 to x = 1), where the function has infinitely many branches. Then we proceed in the same fashion used in the previous examples. The two pictures show two views of the resulting surface.