GATE Questions & Answers of Cauchy's integral formula

What is the Weightage of Cauchy's integral formula in GATE Exam?

Total 3 Questions have been asked from Cauchy's integral formula topic of Complex Analysis subject in previous GATE papers. Average marks 1.00.


$\Large{f\left(z\right)=\frac1{z+1}-\frac2{z+3}}.$ If C is a counterclockwise path in the z-plane such that $\mid z+1\mid=1$, the value of $\frac1{2\pi j}\oint_Cf\left(z\right)dz$

The value of the integral $\underset c{\oint\;}\frac{-3z+4}{\left(z^2+4z+5\right)}dz$ where c is the circle z=1 is given by

If fz=c0+c1z-1, then ${\Large{\underset{circle}{\underset{unit}{\oint}}\frac{1+f\left(z\right)}zdz}}$ is given by