16. Generalize Example 5.2, where the
replaced by . Illustrate
what this means.
See text and/or instructor's solution manual.
Answer. The image region is basically the same as in Example 5.2 in Section 5.1, as the complex exponential is periodic, with period .
a rectangle ,
Show that the transformation maps the rectangle onto a portion of an annular region bounded by two rays.
The image points in the w plane satisfy the following relationships involving the modulus and argument of w:
which is a portion of the annulus in the w plane subtended by the rays .
As an illustration, consider the rectangle .
The rectangle , and its image .
This solution is complements of the authors.
(c) 2008 John H. Mathews, Russell W. Howell