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

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Discussion Overview

The discussion revolves around the use of the color domain method for graphing complex functions in polar coordinates. Participants explore how to represent complex functions visually, particularly through the use of color to indicate different aspects of the functions.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that graphing a complex function typically requires a four-dimensional system but mentions encountering graphs in polar coordinates using a color domain method.
  • Another participant explains that the x and y axes represent the complex plane, while the z axis indicates the real part of the function, with colors representing the imaginary part, suggesting an analogy to wavelength ordering.
  • A request for further explanations is made, indicating a desire for deeper understanding of the concepts involved.
  • Another participant prompts for clarification on what specific aspects are unclear, indicating an interactive nature of the discussion.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants express varying levels of understanding and seek further clarification on the concepts presented.

Contextual Notes

Participants have not fully defined the assumptions underlying the color domain method or the specific mathematical steps involved in graphing complex functions in this manner.

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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