1
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
$$48\,\pi i$$
2
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

A
$${1 \over 2}i$$
B
$${2 \over 3}i$$
C
$${3 \over 4}i$$
D
$${4 \over 5}i$$
3
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
$${{12} \over {13}}$$
4
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$S$$ be the set of points in the complex plane corresponding to the unit circle. $$\left( {i.e.,\,\,S = \left\{ {z:\left| z \right| = 1} \right\}} \right.$$ Consider the function $$f\left( z \right) = z{z^ * }$$ where $${z^ * }$$ denotes the complex conjugate of $$z.$$ The $$f(z)$$ maps $$S$$ to which one of the following in the complex plane?
A
unit circle
B
horizontal axis line segment from origin to $$(1, 0)$$
C
the point $$(1, 0)$$
D
the entire horizontal axis
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