Paper 3, Section I, 5D5 \mathrm{D}

Complex Methods
Part IB, 2009

Use the residue calculus to evaluate (i) Cze1/zdz\oint_{C} z e^{1 / z} d z and (ii) Czdz14z2\oint_{C} \frac{z d z}{1-4 z^{2}},

where CC is the circle z=1|z|=1.