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 fz=z2z2-1,in the counterclockwise direction, around z-1=1,is

z2-4z2+4dz evaluated anticlockwise around the circle z-i=2 ,where i=-1, is


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