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Recent questions tagged cauchys-integral-theorem
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GATE Electrical 2020 | Question: 5
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is: $\int _{C}\frac{z^{2}+1}{z^{2}-2z}\:dz$ $8\pi i$ $-8\pi i$ $-\pi i$ $\pi i$
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is:$$\int _{C}\frac{z^{2}+1}{z...
go_editor
1.9k
points
go_editor
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Feb 28, 2020
Complex Variables
gate2020-ee
complex-variables
cauchys-integral-theorem
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0
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2
GATE Electrical 2019 | Question: 27
The closed-loop line integral $\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$ evaluated Counter-clockwise, is $+8 j \pi$ $-8 j \pi$ $-4 j \pi$ $+4 j \pi$
The closed-loop line integral $$\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$$evaluated Counter-clockwise, is $+8 j \pi$$-8 j \pi$$-4 j \pi$$+4 j \pi$
Arjun
15.9k
points
Arjun
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Feb 12, 2019
Complex Variables
gate2019-ee
complex-variables
cauchys-integral-theorem
line-integral
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0
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3
GATE Electrical 2012 | Question: 3
Given $f(z) = \dfrac{1}{z+1} – \dfrac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$-plane such that $\mid z+1 \mid =1$, the value of $\dfrac{1}{2 \pi \: j} \oint_c f(z) dz$ is $-2$ $-1$ $1$ $2$
Given $f(z) = \dfrac{1}{z+1} – \dfrac{2}{z+3}$. If $C$ is a counterclockwise path in the $z$-plane such that $\mid z+1 \mid =1$, the value of $\dfrac{1}{2 \pi \: j} \oi...
Andrijana3306
1.4k
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Andrijana3306
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Mar 23, 2018
Complex Variables
gate2012-ee
complex-variables
cauchys-integral-theorem
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0
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0
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4
GATE Electrical 2018 | Question: 35
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^2-3z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is $1$ $0$ $-1$ $-2$
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^2-3z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is$1$$0$$-1$$-2$
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Complex Variables
gate2018-ee
complex-variables
cauchys-integral-theorem
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0
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0
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5
GATE Electrical 2018 | Question: 13
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is $\frac{\pi i}{2} \\ $ $2 \pi i\\$ $ – \frac{\pi i}{2}\\$ $-2 \pi i$
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is$\frac{\pi i}...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Complex Variables
gate2018-ee
complex-variables
cauchys-integral-theorem
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0
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0
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6
GATE Electrical 2013 | Question: 36
$\displaystyle{}\int \frac{z^2-4}{z^2+4}\: dz$ evaluated anticlockwise around the circle $\mid z-i \mid=2$ , where $i=\sqrt{-1}$, is $-4\pi$ $0$ $2+\pi$ $2+2i$
$\displaystyle{}\int \frac{z^2-4}{z^2+4}\: dz$ evaluated anticlockwise around the circle $\mid z-i \mid=2$ , where $i=\sqrt{-1}$, is$-4\pi$$0$$2+\pi$$2+2i$
piyag476
1.6k
points
piyag476
asked
Feb 11, 2017
Complex Variables
gate2013-ee
complex-variables
cauchys-integral-theorem
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0
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0
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7
GATE Electrical 2014 Set 3 | Question: 26
Integration of the complex function $f(z)=\dfrac{z^2}{z^2-1}$ , in the counterclockwise direction, around $\mid z-1 \mid = 1$, is $-\pi i$ $0$ $\pi i$ $2 \pi i$
Integration of the complex function $f(z)=\dfrac{z^2}{z^2-1}$ , in the counterclockwise direction, around $\mid z-1 \mid = 1$, is$-\pi i$$0$$\pi i$$2 \pi i$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Complex Variables
gate2014-ee-3
complex-variables
complex-functions
cauchys-integral-theorem
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