1. The problem statement, all variables and given/known data I just wrote a test and was wondering if I got these questions right, I already solved them, please see the attached pictures below. Here are the questions; sorry for non-latex form 1) Let gamma be a positively oriented unit circle (|z|=1) in C solve: i) integral of cos(z+11)/(z^2-23) along gamma ii) integral of cos(z+11)/(z^2-6z) along gamma 2) Find all possible analytic functions f(z) such that |sin 7z| < |f(z)| 3) Draw a closed curve gamma in C\<0,1> such that its winding numbers at 0 is 1 and at 1 is -2. 4) Draw 4 pairwise non-homotopic closed curves in C\<0> 3. The attempt at a solution Here are the pictures: Are these correct? Please let me know if my writing is ineligible. Thanks in advance.