Example 2.22.  Show that the image of the right half plane    under the mapping    is the closed disk    in the w-plane.  

Explore Solution 2.22.

Enter the function f[z] and find its inverse.

Solve for the inverse function and the real and imaginary parts.

Now find the image of the right half plane  .  

This last inequality    is the same as    and is the disk of radius 1 centered at  w = 1  in the w-plane.

We see that the image of the right half plane   under the reciprocal transformation     is the disk    in the w-plane.

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