Example 2.11.  Show that the image of the right half plane    under the linear transformation    is the half plane  .  

Explore Solution 2.11.

Enter the function w = f[z].

Solve for the inverse function, i.e. solve for  z  in terms of  w.  

To solve for ,  we use the computations.

Or the following commands will also find the solution.

Which is the right half plane    in the w-plane.  Use Mathematica to graph the transformation.

We see that the image of the right half plane    under the linear transformation    is the half plane  .  

(c) 2006 John H. Mathews, Russell W. Howell