Find a conformal map of the horizontal strip {-A < Im < A} onto the right half-plane (Rew > 0}. Hint. Recall the discussion of the exponential function, or refer to the preceding problem. Solution (A. Kumjian) FIGURE II.6.4az FIGURE II.6.4aw It is clearly intended that A >0 so we will assume this. We define the map h: C C by h() = e for all C. Then h' (2)= 2A -e for all C. Hence, h is analytic with a nowhere vanishing derivative and so h is conformal. Note that the exponential functions maps the horizontal strip { EC:-/2