1
GATE EE 2021
MCQ (Single Correct Answer)
+2
-0.67

Let $(-1-j),(3-j),(3+j)$ and $(-1+j)$ be the vertices of rectangle $C$ in the complex plane. Assuming that $C$ is traversed in counter-clockwise direction, the value of contour integral $\oint_C \frac{d z}{z^2(z-4)}$ is

A

$\frac{j \pi}{2}$

B

0

C

$\frac{-j \pi}{8}$

D

$\frac{j \pi}{16}$

2
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The value of the contour integral in the complex - plane $$\oint {{{{z^3} - 2z + 3} \over {z - 2}}} dz$$ along the contour $$\left| z \right| = 3,$$ taken counter-clockwise is
A
$$ - 18\,\pi i$$
B
$$0$$
C
$$14$$ $$\pi i$$
D
$$48\,\pi i$$
3
GATE EE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the line integral $${\rm I} = \int\limits_c {\left( {{x^2} + i{y^2}} \right)dz,} $$ where $$z=x+iy.$$ The line $$c$$ is shown in the figure below. GATE EE 2017 Set 1 Engineering Mathematics - Complex Variable Question 12 English

The value of $${\rm I}$$ is

A
$${1 \over 2}i$$
B
$${2 \over 3}i$$
C
$${3 \over 4}i$$
D
$${4 \over 5}i$$
4
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $$\oint\limits_c {{{2z + 5} \over {\left( {z - {1 \over 2}} \right)\left( {{z^2} - 4z + 5} \right)}}} dz$$ over the contour $$\left| z \right| = 1,$$ taken in the anti-clockwise direction, would be
A
$${{24\pi i} \over {13}}$$
B
$${{48\pi i} \over {13}}$$
C
$${{24} \over {13}}$$
D
$${{12} \over {13}}$$

GATE EE Subjects

Browse all chapters by subject