Obtain the laurent series the following functions frac for

Max. Marks: 10

Q 1. Integrate the given function around the given curve traversed in counter-clockwise direction:

for

1. 0 < |z| < 1

1. $f(z) = \frac{1}{\sin\sin\ z\ \ z\ }$ at $z = \frac{\pi}{4}$

2. $f(z) = \frac{e^{z}}{z^{2} + 4}$ at z = 2i