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Since every compex number can be described by angle and distance, rather than real and imaginary value, have anyone tried visually rendering them this way? Letting the x dimension in the image represent the angle, and y the distance, instead of real and imaginary part.... 

"have anyone tried visually rendering them this way? Letting the x dimension in the image represent the angle, and y the distance"

It isn't that interesting really, just an unwrapping of the mandelbrot (if that's what you're referring to), but the topology of the shape doesn't change. In fact most zooms will look almost identical, just rotated or scaled.
It might be interesting to add C as a vector in this (angle,radius) space, which would give a different fractal.
i.e. for every C = (angle, radius), iterate (Z^2) rotated by angle, expanded by radius

Can you show some picture examples?

Rieman-Sphere was tested a bunch of times, afaik...