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Evaluate the integral
written 5.1 years ago by | modified 2.1 years ago by |
Evaluate $\int_{c} \cfrac{dz}{z^{3} (z+4)} $ where c is the circle $|z|=2$.
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written 5.1 years ago by | modified 2.1 years ago by |
Evaluate $\int_{c} \cfrac{dz}{z^{3} (z+4)} $ where c is the circle $|z|=2$.
written 5.1 years ago by |
Solution:
$|z|=2$ is a circle with center at the origin and radius 2.
There are two poles at z=0 and z=-4.
When pole z=0 lies inside the circle and pole z=-4 lies outside the circle.
$\therefore z^{3}$ gives the highest order of pole, i.e., n=3.
$\therefore$ We take, $f(z)=\cfrac{1}{z+4}$ which …