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timeforchg · Aug 28, 2012, 02:34 AM

Determine the location and nature of singularities in the finite z plane of the following functions:
(a) f(z) = ( $z^{2}$ - 1) sin(z)/[z(z+1)(z+2)(z-3)]
(b) g(z) = [1 + cos(z)]/ $z^{8}$

Using Cauchy's intergral formulae, referring to the above functions,
Evaluate
i) $\oint_{c}^{}$ f(z) dz, with C : | z + j | = 4 , traversed positively (CCW),
ii) $\oint_{c}^{}$ g(z) dz, with C: | z - 1 | = 2, traversed positively (CCW).

In each case, sketch the required contour C, carefully showing its direction.

JudyKayTee · Aug 28, 2012, 06:38 AM

Originally Posted by timeforchg

Determine the location and nature of singularities in the finite z plane of the following functions:
(a) f(z) = ( $z^{2}$ - 1) sin(z)/[z(z+1)(z+2)(z-3)]
(b) g(z) = [1 + cos(z)]/ $z^{8}$

Using Cauchy's intergral formulae, referring to the above functions,
Evaluate
i) $\oint_{c}^{}$ f(z) dz, with C : | z + j | = 4 , traversed positively (CCW),
ii) $\oint_{c}^{}$ g(z) dz, with C: | z - 1 | = 2, traversed positively (CCW).

In each case, sketch the required contour C, carefully showing its direction.

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