Conformal Mappings

 

Example 2.20. Find the image of the plane cut along the negative x-axis under the mappings
[Graphics:c14.txtgr1.gif], and
[Graphics:c14.txtgr2.gif].

We investigate this mapping with the following graphs for the image of the disk |z| < 4.

(a) Using [Graphics:c14.txtgr3.gif] we obtain:

 

The branch w = z1/2.

 

[Graphics:c14.txtgr6.gif]

 

The branch w = - z1/2.

 

 

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 (c) John Mathews, 1998, 2006