Example 2.9. Show that the linear transformation w = i z + i
maps the right half plane Re(z) > 1 onto the upper half plane Im(w) > 2.
To express x > 1, we use the computations.
This solution is the upper half plane Im(w) > 2.
![[Graphics:c2.txtgr2.gif]](c2.txtgr2.gif){kind=small}
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(c) John Mathews, 1998, 2006
![[Graphics:c2.txtgr1.gif]](c2.txtgr1.gif)
![[Graphics:c2.txtgr3.gif]](c2.txtgr3.gif){kind=small}