4. Integrate the following functions around the contour C which is a circle of radius 3/2...

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4. Integrate the following functions around the contour C which is a circle of radius 3/2 centred on the origin. [In each case draw a sketch and list clearly the singularities of the integrand lying within C and calculate the residues at each of these singularities doing so in the most efficient way. The values of the integral should follow rapidly.] (a)* 1 (3z + 2)(2 2)' (c) * 2 2 2+2 - z(1 2)' (e)* z +9 eiz (i)* 922 +47 (k)* ez 1 z2 (m)* 2 1 - 24' cosh 21 z Z " (p)* 27 (x + 1) 4. Integrate the following functions around the contour C which is a circle of radius 3/2 centred on the origin. [In each case draw a sketch and list clearly the singularities of the integrand lying within C and calculate the residues at each of these singularities doing so in the most efficient way. The values of the integral should follow rapidly.] (a)* 1 (3z + 2)(2 2)' (c) * 2 2 2+2 - z(1 2)' (e)* z +9 eiz (i)* 922 +47 (k)* ez 1 z2 (m)* 2 1 - 24' cosh 21 z Z " (p)* 27 (x + 1)