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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

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