Riemann surfaces

Real part and imaginary part of the continuation of over the . The imaginary part is a faithful representation of the Riemann surface of .

Real part and imaginary part of the continuation of over the . The viewpoint is from the lower half‐plane. The single square root branch point at that connects two sheets and the logarithmic branch point that connects infintely many sheets are visible.

Imaginary parts of the continuation of over the Riemann sphere. The single square root branch point at that connects two sheets and the logarithmic branch point at the south pole that connects infintely many sheets are visible.