Riemann Surface of Log Hahnemühle German Etching Print

The real exponential function is monotone, and therefore invertible. The complex exponential function, by contrast, is periodic with imaginary period, and therefore fails to be invertible in the same way circular functions in precalculus fail to be invertible. Each non-zero complex number has infinitely many complex logarithms. There is a continuous choice of logarithm on the "slit plane" with the non-positive real axis removed, and other branches are obtained by adding whole multiples of the period. The branches can be assembled into a smooth "helical" surface as shown in the image. Walking around the origin in the domain causes the logarithm to pass from one branch to the next.

All our prints are available on a range of matt and lustre finishes, each carefully profiled for fantastically accurate and consistent reproductions using giclée printing techniques.

• Hahnemühle German Etching (310gsm)
• A premium fine art paper with a velvety surface perfect for archival quality reproductions.