Problem 2 (Contour integrals) (a) Evaluate the integral S where y is the regular polygon obtained by joining all ninth roots of unity in counter- clockwise order. (b) Evaluate the integrals where are as in part (b). esin(z) dz 23 9z2+262 - 24 1 Lusti z + i Y+ dz z² +1 Suz and 7- where is the simple closed curve given by the locus of a point on the perimeter of a circle of radius 99.94 that rolls with unit speed exactly once around the circle of radius 99.94 centred at Fi. (c) Evaluate the integrals and Z L 1 i' dz z²+1

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