Exercise 19.  Explain how the complex function    and the real function    are different.  How are they similar?  

Solution 19.

See text and/or instructor's solution manual.

Solution.   Let      and   .  

They are similar in the following:

             and   .  

             and   .  

             and   .

             and   

             and   

          The rules for exponents apply to both functions.

They are different in the following regard:

            is periodic with period  .

            maps the two dimensional complex z-plane onto the two dimensional w-plane.

Can you think of any more?

This solution is complements of the authors.

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