1
GATE EE 2026
Numerical
+2
-0

The magnitude of the contour integral

$$ \int_c \frac{(z+1)^2}{(z-i)(z-2)} d z $$

over the contour $C:|z-2-i|=\frac{3}{2}$ is $\_\_\_\_$ . [Round off to two decimal places]

Note : $z$ is a complex variable and $i=\sqrt{-1}$.

Your input ____
2
GATE EE 2025
Numerical
+2
-0
Let $C$ be a clockwise oriented closed curve in the complex plane defined by $|\lambda|=1$. Further, let $f(x)=j z$ be a complex function, where $j=\sqrt{-1}$. Then, $\oint_C f(z) d z=$ ___________ .
Your input ____
3
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

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

4
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
$$48\,\pi i$$

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