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Recent questions and answers in Complex Analysis
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1
GATE EC 2021  Question: 26
Consider the integral $\oint _{c}\frac{sin\left ( x \right )}{x^{2}\left ( x^{2}+4 \right )}dx$ where $C$ is a counterclockwise oriented circle defined as $\left  xi \right =2$. The value of the integral is $\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
asked
Feb 20
in
Complex Analysis
by
Arjun
(
4.4k
points)

68
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gateec2021
complexanalysis
+2
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2
GATE ECE 2019  Question: 1
Which one of the following functions is analytic over the entire complex plane? $\ln(z)$ $e^{1/z}$ $\frac{1}{1z}$ $\cos(z)$
asked
Feb 12, 2019
in
Complex Analysis
by
Arjun
(
4.4k
points)

216
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gate2019ec
complexanalysis
0
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0
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3
GATE ECE 2016 Set 3  Question: 2
For $f(z)= \large\frac{\sin(z)}{z^2}$, the residue of the pole at $z = 0$ is _______
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

20
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gate2016ec3
numericalanswers
complexanalysis
0
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0
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4
GATE ECE 2016 Set 3  Question: 29
The values of the integral $\large\frac{1}{2\pi j}\oint_c\frac{e^z}{(z2)} \small dz$ along a closed contour $c$ in anticlockwise direction for the point $z_0=2$ inside the contour $c$, and the point $z_0=2$ outside the contour $c$, respectively,are $(i)2.72, \: (ii) 0$ $(i)7.39, \: (ii) 0$ $(i)0, \: (ii) 2.72$ $(i)0, \: (ii) 7.39$
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

12
views
gate2016ec3
complexanalysis
0
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0
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5
GATE ECE 2016 Set 2  Question: 2
Consider the complex valued function $f(z)=2z^{3}+b\mid z \mid^{3}$ where $z$ is a complex variable. The value of $b$ for which function $f(z)$ is analytic is _________
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

17
views
gate2016ec2
numericalanswers
complexanalysis
0
votes
0
answers
6
GATE ECE 2016 Set 2  Question: 27
Suppose $C$ is the closed curve defined as the circle $x^{2}+y^{2}=1$ with $C$ oreinted anticlockwise. The value of $\oint$ ( $xy^{2}$ $dx$ + $ x^{2}y$ $dy$ )over the curve $C$ equals _________
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

12
views
gate2016ec2
numericalanswers
complexanalysis
0
votes
0
answers
7
GATE ECE 2016 Set 1  Question: 6
Which one of the following is an eigen function of the class of all continuoustime, linear, timeinvariant systems ($u(t)$ denotes the unitstep function)? $e^{j\omega_0t}u(t)$ $\cos(\omega_0t)$ $e^{j\omega_0t}$ $\sin(\omega_0t)$
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
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15.8k
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17
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gate2016ec1
complexanalysis
0
votes
0
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8
GATE ECE 2016 Set 1  Question: 28
In the following integral, the contour $C$ encloses the points $2 \pi j$ and $ 2\pi j$ $\frac{1}{2\pi}\oint_C\frac{\sin z}{(z2\pi j)^3} \,dz$ The value of the integral is _________
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

19
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gate2016ec1
numericalanswers
complexanalysis
0
votes
0
answers
9
GATE ECE 2015 Set 3  Question: 3
If $C$ is a circle of radius $r$ with centre $z_{0},$ in the complex $z$plane and if $n$ is a nonzero integer, then $\oint _{C}\frac{dz}{(zz_{0})^{n+1}}$ equals $2\pi n j$ $0$ $\frac{nj}{2\pi}$ $2\pi n$
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

15
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gate2015ec3
vectoranalysis
0
votes
0
answers
10
GATE ECE 2015 Set 3  Question: 51
The complex envelope of the bandpass signal $x(t)=\sqrt{2}\left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)\sin (\pi t  \dfrac{\pi}{4}),$ centered about $f=\dfrac{1}{2}\:Hz,$ is $\left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)e^{j\dfrac{\pi}{4}}$ ... $\sqrt{2} \left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)e^{j\dfrac{\pi}{4}}$
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

11
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gate2015ec3
complexanalysis
0
votes
0
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11
GATE ECE 2015 Set 2  Question: 3
Let $f(z)=\dfrac{az+b}{cz+d}.$ If $f(z_{1})=f(z_{2})$ for all $z_{1}\neq z_{2},a=2,b=4$ and $c=5,$ then $d$ should be equal to ________.
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

11
views
gate2015ec2
numericalanswers
complexanalysis
0
votes
0
answers
12
GATE ECE 2015 Set 2  Question: 28
If $C$ denotes the counterclockwise unit circle, the value of the contour integral $\dfrac{1}{2\pi j}\oint_{C} Re\{z\}dz$ is __________.
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
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15.8k
points)

16
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gate2015ec2
numericalanswers
complexanalysis
0
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0
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13
GATE ECE 2015 Set 1  Question: 4
Let $z=x+iy$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE? The residue of $\frac{z}{z^21}$ at $z=1$ is $1/2$ $\oint_C z^2 dz=0$ $\frac{1}{2 \pi i} \oint_C \frac{1}{z} dz =1$ $\overline{z}$ (complex conjugate of $z$ is an analytical function
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

19
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gate2015ec1
complexanalysis
analyticfunctions
0
votes
0
answers
14
GATE ECE 2014 Set 2  Question: 27
The real part of an analytic function $f(z)$ where $z = x + jy$ is given by $e^{y} \cos(x)$. The imaginary part of $f(z)$ is $e^{y} \cos( x )$ $e^{y} \sin( x )$ $e^{y} \sin ( x )$ $e^{y} \sin (x )$
asked
Mar 26, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

33
views
gate2014ec2
analyticfunctions
complexanalysis
0
votes
0
answers
15
GATE ECE 2014 Set 1  Question: 3
$C$ is a closed path in the $z$plane given by $\mid z \mid = 3.$ The value of the integral $\displaystyle{}\oint_{C}\bigg(\dfrac{z^{2}z+4j}{z+2j}\bigg)dz$ is $4\pi(1+j2)$ $4\pi(3j2)$ $4\pi(3+j2)$ $4\pi(1j2)$
asked
Mar 26, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

16
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gate2014ec1
complexanalysis
0
votes
0
answers
16
GATE ECE 2014 Set 1  Question: 27
For a function $g(t),$ it is given that $\int_{ \infty}^{ + \infty} g(t)e^{j\omega t}\:dt = \omega e^{2\omega^{2}}$ for any real value $\omega.$ If $y(t) = \int_{ \infty}^{t}\:g(\tau)\:d\tau,$ then $\int_{ \infty}^{ + \infty}y(t)dt$ is $0$ $j$ $\frac{j}{2}$ $\frac{j}{2}$
asked
Mar 26, 2018
in
Complex Analysis
by
Milicevic3306
(
15.8k
points)

15
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gate2014ec1
complexanalysis
0
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0
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17
GATE ECE 2018  Question: 51
The contour $C$ given below is on the complex plane $z=x+j y,$ where $j=\sqrt{1}.$ The value of the integral $\displaystyle{}\dfrac{1}{\pi j}\oint _{C}\dfrac{dz}{z^{2}1}$ is _______.
asked
Feb 19, 2018
in
Complex Analysis
by
gatecse
(
1.5k
points)

155
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gate2018ec
numericalanswers
complexanalysis
0
votes
0
answers
18
GATE ECE 2017 Set 2  Question: 4
The residues of a function $f(z)=\frac1{(z4)(z+1)^3 }$ are $\frac{1}{27}$ and $\frac{1}{125} \\$ $\frac{1}{125}$ and $\frac{1}{125} \\$ $\frac{1}{27}$ and $\frac{1}{5} \\$ $\frac{1}{125}$and $\frac{1}{5}$
asked
Nov 23, 2017
in
Complex Analysis
by
admin
(
2.8k
points)

27
views
gate2017ec2
complexanalysis
0
votes
0
answers
19
GATE ECE 2017 Set 1  Question: 48
Which one of the following options correctly describes the locations of the roots of the equation $s^{4}+s^{2}+1=0$ on the complex plane? Four left half plane(LHP) roots One right half plane(RHP) root,one LHP root and two roots on the imaginary axis Two RHP roots and two LHP roots All four roots are on the imaginary axis
asked
Nov 17, 2017
in
Complex Analysis
by
admin
(
2.8k
points)

50
views
gate2017ec1
complexanalysis
0
votes
0
answers
20
GATE ECE 2017 Set 1  Question: 28
Let $I=\int_{c}\left ( 2zdx+2ydy+2xdx \right )$ where $x,y,z$ are real, and let $C$ be the straight line segment from point $A:(0,2,1)$ to point $B:(4,1,1)$.The value of $I$ is ____________.
asked
Nov 17, 2017
in
Complex Analysis
by
admin
(
2.8k
points)

62
views
gate2017ec1
complexanalysis
numericalanswers
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