19. Explain how the complex
the real function are
different. How are they similar?
See text and/or instructor's solution manual.
Solution. Let and .
They are similar in the following:
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