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.
Handmade in the UK by specialist picture framers using premium fine art paper with a gently textured surface and satin finish, high-quality wood, and an FSC certified off-white mat. Delivered ready for hanging.