engineering recuitment GATE ME 2023-24 Test Series Engineering Mathematics Complex Variables Residue Theorem
Let \(I = \mathop \smallint \limits_C^\; \frac{{f\left( z \right)}}{{\left( {z - 1} \right)\left( {z - 2} \right)}}dz,\) where \(f\left( z \right) = \sin \frac{{\pi z}}{2} + \cos \frac{{\pi z}}{2}\) and C is the curve |z| = 3 oriented anti-clockwise. Then the value of I is
1
4π i
2
0
3
-2π i
4
-4π i