Mobius Transformation for Im(z) > 2 to |w-2| < 3

  • Thread starter Thread starter latentcorpse
  • Start date Start date
  • Tags Tags
    Transformation
Click For Summary

Homework Help Overview

The discussion revolves around finding a Mobius Transformation that maps the upper half-plane defined by Im(z) > 2 to a circular region defined by |w - 2| < 3. Participants are exploring the properties and requirements of Mobius transformations in this context.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the requirement of selecting three points to define the transformation and the preservation of orientation. There is a suggestion to choose specific points in the upper half-plane and their corresponding images in the circular region.

Discussion Status

The discussion is ongoing, with participants sharing ideas about how to select points for the transformation. Some guidance has been provided regarding the selection of points and the orientation preservation, but no consensus or complete solution has emerged yet.

Contextual Notes

There is an emphasis on the properties of Mobius transformations and the need for specific point selection, but the participants have not yet clarified all necessary details or constraints for the transformation.

latentcorpse
Messages
1,411
Reaction score
0
I'm pretty stuck on this. I need to find a Mobius Transformation f such that

[itex]f: \{ z: Im{z}>2 \} \rightarrow \{ w:|w-2|<3 \}[/itex]

I don't really have any ideas here. My notes aren't really helping here either. Can anybody point me in the right direction?
 
Physics news on Phys.org
Do your notes say that Mobius transformations are determined by 3 images and preserve orientation?
 
yes. i think so. how does this help us though?
 
I think this will work: Pick 3 points on the line I am z = 2 that go in a certain direction. Say you pick them such that the half plane is on their right. For their images under the Mobius transformation, pick 3 points on the circle |w - 2| = 3 such that the interior of the circle is also on their right.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 23 ·
Replies
23
Views
3K
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
7
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
14
Views
4K