Exercise 13.  Let  .   Show that    is continuous for all values of z.  

Solution 13.

See text and/or instructor's solution manual.

Solution.  Consider the real and imaginary parts  .  

The real part    is continuous since  .  

The imaginary part    is continuous since  .  

The function     is continuous by Theorem 2.1.

This solution is complements of the authors.

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