Exercise 7.  Establish the following minimum modulus principle.  

7 (a).  Let    be analytic and nonconstant in the domain  D.  

If    for all  z in  D,  where  ,  then    does not attain a minimum value at any point    in  D.

Solution 7 (a).

See text and/or instructor's solution manual.

Solution.   If    for all  z  in  D,  where  ,  then the function    is analytic in D.  

Apply Theorem 6.16 (Maximum Modulus Principle) to the function    to get your result.

This solution is complements of the authors.

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