Exercise 20.  Many texts give an alternative definition for  ,  starting with (5-1) as the definition for  .  

20 (d).  Now use the Cauchy-Riemann equations to conclude from part (c) that

                    .  

Solution 20 (d).

See text and/or instructor's solution manual.

Solution.   From part (c)

          ,           so that

,   ,   ,   .   

The  Cauchy Riemann equations are  

        ,  

        .  

Hence we obtain    .   

This solution is complements of the authors.

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