Solution 16.

Solution.  Since   is a bilinear transformation or Mobius transformation,

the four complex complex constants    have the restriction that  .  

The derivative of   is

                    .

Since  ,  the numerator of   is not equal to zero.  

The denominator of   is equal to zero when , which occurs when .  

The denominator    at all points  .

Hence    at all points  .

Therefore,    is conformal at all points  .

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell