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Recent questions tagged complex-variables
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GATE Chemical 2019 | Question: 27
The value of the complex number $i^{-1/2}$ (where $i=\sqrt{-1}$) is $\frac{1}{\sqrt{2}}\left ( 1-i \right )$$-\frac{1}{\sqrt{2}}i$$\frac{1}{\sqrt{2}}i$$\frac{1}{\sqrt{2}}...
Arjun
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Arjun
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Feb 24, 2019
Complex variables
gate2019
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complex-number
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GATE Chemical 2017 | Question: 2
The real part of $6e^{i\pi /3}$ is _______________.
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Complex variables
gate2017
numerical-answers
complex-variables
complex-number
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GATE Chemical 2016 | Question: 3
What are the modulus $\left ( r \right )$ and argument $\left ( \theta \right )$ of the complex number $3+4i$ ?$r=\sqrt{7}, \theta =tan^{-1}\left ( \frac{4}{3} \right )$$...
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Complex variables
gate2016
complex-variables
complex-number
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GATE Chemical 2015 | Question: 14
A complex-valued function, $f(z)$, given below is analytic in domain $D$:$$f\left ( z \right )=u\left ( x,y\right )+i\nu \left ( x,y\right )\:\:\:\:\:\:\:z=x+iy$$Which of...
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Complex variables
gate2015
complex-variables
complex-valued-function
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GATE Chemical 2015 | Question: 39
For complex variable $z$, the value of the contour integral $\frac{1}{2\pi i} \underset{C}{\int }\frac{e^{-2z}}{z(z-3)}dz$ along the clockwise contour $C:\left | z \right...
Milicevic3306
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Milicevic3306
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Mar 26, 2018
Complex variables
gate2015
numerical-answers
complex-variables
contour-integral
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GATE Chemical 2013 | Question: 26
For the functionf(z) = $\frac{1}{(2-z)(z+2)}$the residue at z = 2 is $\_\_\_\_\_$
Milicevic3306
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Milicevic3306
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Mar 25, 2018
Complex variables
gate2013
numerical-answers
complex-variables
cauchy-residue-theorems
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GATE Chemical 2012 | Question: 29
If $i = \sqrt{-1}$, the value of the integral $$\oint_{c}\dfrac{7z + i}{z(z^2 + 1)}dz \quad\quad\quad\quad|z|<2$$,u...
Milicevic3306
7.9k
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Milicevic3306
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Mar 25, 2018
Complex variables
gate2012
complex-variables
cauchy-residue-theorems
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GATE Chemical 2018 | Question: 31
The decay ratio for a system having complex conjugate poles as $\left ( -\frac{1}{10}+j\frac{2}{15} \right )$ and $\left ( -\frac{1}{10}-j\frac{2}{15} \right )$ is $7\ti...
gatecse
1.4k
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gatecse
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Feb 20, 2018
Complex variables
gate2018
complex-variables
complex-conjugate-poles
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