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.

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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