How Is the Color Domain Used to Graph Complex Functions in Polar Coordinates?

omer21
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As you know to graph a complex function we need four dimensional system,but i encountered with some graphs of complex functions on polar coordinate systems which called "colour domain".
Can somebody explain me what is the colour domain method and how to graph a complex function on a polar coordinate system in that way.

Also, for instance at this link http://www.mathworks.com/products/matlab/demos.html?file=/products/demos/shipping/matlab/cplxdemo.html there are some pretty graphs,what happens there i do not understand ,what is the mentality of plotting this graphs...
 
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The x and y axes are the complex plane for the domain. The z axis tells you what the real part of f(a) is and you color it according to the imaginary part of f(a) (you can imagine the colors being ordered based on wavelength)
 
please more explanations
 
What exactly don't you understand?
 

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