Conformal Mappings

 

Example 2.11. Show that the image of the right half plane Re(z) > 1
under the linear transformation w = (-1+ i) z - 2+3i is the half plane v > u + 7.

[Graphics:c6.txtgr2.gif][Graphics:c6.txtgr1.gif]

Solve for z in terms of w.

[Graphics:c6.txtgr2.gif][Graphics:c6.txtgr3.gif]

Solve for Re(z) > 1.

[Graphics:c6.txtgr2.gif][Graphics:c6.txtgr4.gif]

Which is the right half plane v > 7 + u in the w-plane.

  The transformation w = (-1 + i) z - 2 + 3i.

 

 

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 (c) John Mathews, 1998, 2006