Recent questions and answers in Complex Variables - GO Electrical

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GATE Electrical 2021 | Question: 2
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ ... $p\left ( z \right )=0$ come in conjugate pairs All the roots cannot be real

asked Feb 20 in Complex Variables by Arjun (7.8k points)

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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: $\int _{C}\frac{z^{2}+1}{z^{2}-2z}\:dz$ $8\pi i$ $-8\pi i$ $-\pi i$ $\pi i$

asked Feb 28, 2020 in Complex Variables by jothee (1.8k points)

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GATE Electrical 2019 | Question: 4
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ? $\frac{z^{2}-1}{z} \\ $ $\frac{z^{2}-1}{z+2} \\ $ $\frac{z^{2}-1}{z-0.5} \\ $ $\frac{z^{2}-1}{z+j0.5} $

asked Feb 12, 2019 in Complex Variables by Arjun (7.8k points)

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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 $+8 j \pi$ $-8 j \pi$ $-4 j \pi$ $+4 j \pi$

asked Feb 12, 2019 in Complex Variables by Arjun (7.8k points)

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GATE Electrical 2012 | Question: 2
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{- \pi/2}$ $e^{\pi/2}$ $x$ $1$

asked Mar 24, 2018 in Complex Variables by Andrijana3306 (1.4k points)

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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 $-2$ $-1$ $1$ $2$

asked Mar 24, 2018 in Complex Variables by Andrijana3306 (1.4k points)

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GATE Electrical 2018 | Question: 34
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is $3$ $4$ $5$ $6$

asked Feb 19, 2018 in Complex Variables by Arjun (7.8k points)

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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 $1$ $0$ $-1$ $-2$

asked Feb 19, 2018 in Complex Variables by Arjun (7.8k points)

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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}\\$ $-2 \pi i$

asked Feb 19, 2018 in Complex Variables by Arjun (7.8k points)

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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 $-4\pi$ $0$ $2+\pi$ $2+2i$

asked Feb 12, 2017 in Complex Variables by piyag476 (1.5k points)

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GATE Electrical 2013 | Question: 23
Square roots of $-i$,where $i=\sqrt{-1}$, are $i,-i \\$ $\cos(-\dfrac{\pi }{4} )+i\sin(-\dfrac{\pi }{4})+\cos(\dfrac{3\pi }{4})+i\sin(\dfrac{3\pi }{4}) \\$ $\cos(\dfrac{\pi }{4} )+i\sin(\dfrac{3\pi }{4})+\cos(\dfrac{3\pi }{4})+i\sin(\dfrac{\pi }{4}) \\$ $\cos(\dfrac{3\pi }{4} )+i\sin(-\dfrac{3\pi }{4})+\cos(-\dfrac{3\pi }{4})+i\sin(\dfrac{3\pi }{4})$

asked Feb 12, 2017 in Complex Variables by piyag476 (1.5k points)

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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 $-\pi i$ $0$ $\pi i$ $2 \pi i$

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.3k points)

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GATE Electrical 2014 Set 2 | Question: 4
All the values of the multi-valued complex function $1^i$,where $i=\sqrt{-1}$ are purely imaginary. real and non-negative on the unit circle. equal in real and imaginary parts.

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.3k points)

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14

GATE Electrical 2014 Set 1 | Question: 5
Let $S$ be the set of points in the complex plane corresponding to the unit circle. $(\text{That is}, S = \{z :\:\: \mid z \mid =1\}).$ Consider the function $f(z)=zz^{\ast}$ where $z^{\ast}$ denotes the complex ... following in the complex plane unit circle horizontal axis line segment from origin to $(1, 0)$ the point $(1, 0)$ the entire horizontal axis

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.3k points)

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GATE Electrical 2015 Set 2 | Question: 1
Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE? If $f(z)$ is differentiable at $z_{0}$, then $g(z)$ and $h(z)$ are also differentiable ... $z_{0}$. If $f(z)$ is differentiable at $z_{0}$, then so are its real and imaginary parts

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.3k points)

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GATE Electrical 2016 Set 2 | Question: 6
Consider the function $f(z)=z+z^{*}$ where $z$ is a complex variable and $z^{*}$ denotes its complex conjugate. Which one of the following is TRUE? $f(z)$ is both continuous and analytic $f(z)$ is continuous but not analytic $f(z)$ is not continuous but is analytic $f(z)$ is neither continuous nor analytic

asked Jan 30, 2017 in Complex Variables by makhdoom ghaya (9.3k points)

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Recent questions and answers in Complex Variables

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