Section 3.2, page 115 
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1. (#20)

   Here you need to check and verify that the boundaries of the rectangle
   in the z-plane are mapped to the boundaries of the annulus in the 
   w-plane. So, for example I will demonstrate two of the boundaries.

   a. Lower edge of the rectangle. Parametrize that edge as

      z = x + i 0, with x \in [-1, 1].

      Then,

      w = e^z = e^x is a real number with e^x \in [1/e, e] which is the
      lower right edge of the annulus in the w-plane.

   b. Right edge of the rectangle. Parametrize this edge as

      z = 1 + i \pi t, with t \in [0, 1].

      Then,

      w = e^z = (e) (e^i \pi t) with t \in [0, 1]. Hence, w is a point
      in the semicircle of radius e with its argument changing from 0
      to \pi. This is the outer semicircle of the annulus in the w-plane.

Now you can finish the problem.
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