engineering recuitment GATE EE 2023-24 Test Series Engineering Mathematics Complex Variables Cauchy's Integral Theorem
Evaluate \(\mathop \oint \limits_C \frac{1}{{{{\left( {z - 1} \right)}^3}\left( {z - 3} \right)}}dz\) where C is the rectangular region defined by x = 0, x = 4, y = -1 and y = 1
1
1
2
0
3
\(\frac{\pi }{2}i\)
4
π (3 + 2i)