# GATE Questions & Answers of Cauchy’s Integral Formula

## What is the Weightage of Cauchy’s Integral Formula in GATE Exam?

Total 4 Questions have been asked from Cauchy’s Integral Formula topic of Complex variables subject in previous GATE papers. Average marks 1.75.

The line integral of function F = yzi, in the counterclockwise direction, along the circle x2+y2 = 1 at z = 1 is

Integration of the complex function $f\left(z\right)=\frac{{z}^{2}}{{z}^{2}-1}$,in the counterclockwise direction, around $\left|z-1\right|=1$,is

$\int \frac{{z}^{2}-4}{{z}^{2}+4}dz$ evaluated anticlockwise around the circle $\left|z-i\right|=2$ ,where $i=\sqrt{-1}$, is
f(z)= $\frac{1}{z+1}-\frac{2}{z+3}$. If C is a counterclockwise path in the z-plane such that $\left|z+1\right|=1$, the value of $\frac1{2\pi j}\oint_cf\left(z\right)dz$ is