Solution 11.

See text and/or instructor's solution manual.

Solution.   Use the polar form of the Cauchy-Riemann equations     and     and multiply both sides by r and obtain  

                       and   .   

Differentiate them first with respect to and get  

                       and   .  

Then differentiate them with respect to r and get  

                       and   .

The last equation implies that  ,  and then the result follows:  

                        

This solution is complements of the authors.

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