- #1

mick25

- 13

- 0

## Homework Statement

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>

## The Attempt at a Solution

Here are the pictures:

Are these correct? Please let me know if my writing is ineligible. Thanks in advance.