1
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, $\oint_C f(z) d z=$ ___________ .
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2
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
3
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
4
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.
The value of $${\rm I}$$ is
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