Let A be the strip {z C: 0 < Re(z), 0 Im(z) < 27} and...

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Let A be the strip {z € C: 0 < Re(z), 0≤ Im(z) < 27} and f: C C be the map given by f(z) =i+e-². (a) (3 points) Find the image f(@A), where A is the boundary of A in C. (b) (3 points) Show that for every z EA, we have f(z) - i| < 1. (c) (4 points) Suppose D is the punctured disk {z € C: 0 < z-i| < 1}. Show that for every w E D there exits z € A such that f(z) = w and conclude the image f(A) is D. Let A be the strip {z € C: 0 < Re(z), 0≤ Im(z) < 27} and f: C C be the map given by f(z) =i+e-². (a) (3 points) Find the image f(@A), where A is the boundary of A in C. (b) (3 points) Show that for every z EA, we have f(z) - i| < 1. (c) (4 points) Suppose D is the punctured disk {z € C: 0 < z-i| < 1}. Show that for every w E D there exits z € A such that f(z) = w and conclude the image f(A) is D.

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a 3 points Find the image fOA where OA is the boundary of A in C ANSWER The image of the boundary is ... View the full answer