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This is the color encoding used in the Complex log image above. Each complex value is represented as a particular color. The arg (polar coordinate angle) of the complex number is encoded as the hue of the color. The modulus of the complex number is encoded as the saturation (intensity) of the color.

DescriptionComplex log.jpg	function Log[z] in the complex plane
Date	3 August 2007 (upload date)
Source	Own work  This diagram was created with Mathematica.
Author	Jan Homann; Color encoding image comment author Hal Lane, September 28, 2009

This work has been released into the public domain by its author, Jan Homann. This applies worldwide. In some countries this may not be legally possible; if so: Jan Homann grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.