GATE Engineering Mathematics: Complex Variables: Cauchy's integral theorem – Previous Year Questions
7 GATE previous year questions on Complex Variables: Cauchy's integral theorem (Engineering Mathematics, Electrical Engineering) with answers and explanations, from every paper.
- GATE 2017 EE Q38 – Consider the line integral I = c (x2 + iy2)\,dz, where z = x + iy. The line c is shown in the figure below. [Figure: The x-y plane with a straight…
- GATE 2018 EE Q23 – The value of the integral Cz+1z2-4\,dz in counter clockwise direction around a circle C of radius 1 with center at the point z=-2 is
- GATE 2018 EE Q45 – If C is a circle z =4 and f(z)=z2(z2-3z+2)2, then Cf(z)\,dz is
- GATE 2019 EE Q37 – The closed loop line integral z =5z3+z2+8z+2\,dz evaluated counter-clockwise, is
- GATE 2020 EE Q15 – The value of the following complex integral, with C representing the unit circle centered at origin in the counterclockwise sense, is: Cz2+1z2-2z\,dz
- GATE 2021 EE Q38 – Let (-1-j), (3-j), (3+j) and (-1+j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise…
- GATE 2026 EE Q62 – The magnitude of the contour integral C((z+1)2(z-i)(z-2))dz over the contour C:\ z-2-i =3/2 is . (Round off to two decimal places) Note: z is a…