The Mobius Transformation

 

Chapter 10. Find the image of the quadrant x > 0, y > 0 under [Graphics:m8.txtgr1.gif].

To show S(z) is one-to-one, find the inverse function.

[Graphics:m8.txtgr3.gif][Graphics:m8.txtgr2.gif]

The image is found graphically to be the portion of the unit disk |w|<1 that lies in the upper-half plane Im(w)>0.

[Graphics:m8.txtgr3.gif]

The Mobius transformation [Graphics:m8.txtgr1.gif]. 

 

 

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(c) John Mathews, 1998, 2006