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

In summary, the conversation discusses the use of a four-dimensional system to graph complex functions, as well as the use of a "colour domain" method to graph complex functions on a polar coordinate system. The speaker also mentions a link with examples of these types of graphs and asks for further explanation on the process of plotting them. The color of the graph is determined by the imaginary part of the function, with the colors being ordered based on wavelength. The speaker requests more clarification on this topic.
  • #1
omer21
25
0
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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  • #2
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)
 
  • #3
please more explanations
 
  • #4
What exactly don't you understand?
 

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

1. What is a complex function?

A complex function is a mathematical function that takes complex numbers as inputs and outputs complex numbers. It can be represented by a graph in the complex plane, with the real and imaginary parts plotted on the x and y axes respectively.

2. How do you graph a complex function?

To graph a complex function, you plot the complex numbers in the function on the complex plane. The real part is plotted on the x-axis and the imaginary part on the y-axis. The resulting graph will show a visual representation of the function in the complex plane.

3. What are the benefits of graphing complex functions?

Graphing complex functions allows for a better understanding of their behavior and properties. It can also aid in visualizing complex numbers and their relationships with each other.

4. How can you determine the domain and range of a complex function from its graph?

The domain of a complex function is all the possible inputs, or complex numbers, that can be plugged into the function. The range is all the possible outputs, or complex numbers, that the function can produce. These can be determined by looking at the x and y values on the graph.

5. Are there any limitations to graphing complex functions?

One limitation of graphing complex functions is that the graph can only show a two-dimensional representation of a function that operates in a higher dimensional space. Additionally, some complex functions may be difficult to graph or may not have a clear graph due to their complex nature.

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