engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Complex Variables Residue Theorem
Let C be the simple, positively oriented circle of radius 2 centred at the origin in the complex plane. Then
\(\frac{2}{{\pi i}}\smallint \left( {z{e^{\frac{1}{z}}} + \tan \left( {\frac{z}{2}} \right) + \frac{1}{{\left( {z - 1} \right){{\left( {z - 3} \right)}^2}}}} \right)dz\) equals ________.Enter numerical value using the virtual keypad. Round off where necessary.