(All images created with MATLAB® software)

One of the branches used in the construction of the Riemann Surface for (z^{2}-1)^{1/2}. The surface produced by this branch (shown here) must be joined with the surface produced by the other branch (which is just the negative of this one) along the discontinuities on the branch cuts, to produce the desired Riemann Surface.

Picture obtained using the script RiemannSur in the Athena 18.04 MATLAB® Toolkit.

Figure 1: Side view of the Riemann Surface for the function f(z)=(z^{2}-1)^{1/2}