Graphing functions of two complex variables.

In summary, the conversation is about finding a graphical representation of a function involving two complex numbers. The function is f(z,w) = \sqrt{(\log |z+w|)^2 + (\log |z-\overline{w}|)^2}, and the person is struggling to figure out how to do it by hand or in Maple. However, it is mentioned that the domain is four dimensional, making it difficult to visualize. Despite this challenge, the person expresses gratitude for any help.
  • #1
pbandjay
118
0
Hello,

I have come across this problem in my studies where I need to try to come up with a graph of a function involving two complex numbers. I have been trying to figure this out for a while now, but I am not sure how to do it. Is there any way to do this type of thing by hand or in Maple?

The type of thing I need to find a graphical representation of is:

[tex]f(z,w) = \sqrt{(\log |z+w|)^2 + (\log |z-\overline{w}|)^2}[/tex]

This is a bit simpler than the ones I have, but it's similar. If anyone can help, thank you in advance!
 
Mathematics news on Phys.org
  • #2
You're not going to have much luck as the domain is four dimensional and therefore difficult to visualize.
 
  • #3
That's what I was afraid of... Thank you anyways. :smile:
 

1. What are complex variables?

Complex variables are numbers that have both a real and imaginary component. They are typically represented in the form a + bi, where a is the real component and bi is the imaginary component multiplied by the imaginary unit i.

2. How are functions of two complex variables graphed?

Functions of two complex variables are graphed on a complex plane, where the horizontal axis represents the real component and the vertical axis represents the imaginary component. The function is then plotted as a surface on this plane.

3. What is the significance of the real and imaginary parts in a graph of a function of two complex variables?

The real and imaginary parts of a function of two complex variables determine the shape and behavior of the graph. The imaginary part represents the vertical displacement of the graph, while the real part represents the horizontal displacement.

4. How do you interpret the graph of a function of two complex variables?

The graph of a function of two complex variables can be interpreted in a similar way to a graph of a function of one variable. The height of the surface represents the output of the function at a particular point on the complex plane, and the shape of the surface can provide insights into the behavior of the function.

5. Can functions of two complex variables be visualized with traditional 2D graphs?

No, functions of two complex variables cannot be accurately represented with traditional 2D graphs. They require a complex plane to be visualized, as both the real and imaginary components must be taken into account.

Similar threads

I Is it valid to express a complex number as a vector?
    • General Math
Replies
8
Views
1K
A Help needed with derivation: solving a complex double integral
    • General Math
Replies
1
Views
729
B Looking for free graphing calculator for two-variable inequality
    • General Math
Replies
4
Views
987
B Principal square root of a complex number, why is it unique?
    • General Math
Replies
13
Views
3K
B How can complex numbers be elevated to complex powers?
    • General Math
Replies
12
Views
2K
B Difference between functions and variables
    • General Math
Replies
13
Views
2K
I Can a Circular Function with Complex Variable Represent a 3D Graph?
    • General Math
Replies
7
Views
1K
A Array variable of envelope function (parameter representation)
    • General Math
Replies
2
Views
913
B Choosing which variable is the dependent or independent variable
    • General Math
Replies
16
Views
1K
I When is it preferable to use semi-log and log-log graphs?
    • General Math
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top