GATE CE

Complex Variable

Engineering Mathematics

(Past Years Questions)

Marks 1

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Consider the following complex function $$f\left( z \right) = {9 \over {\left( {z - 1} \right)\left( {z + 2} \right)}}.$...
GATE CE 2015 Set 1
$$z = {{2 - 3i} \over { - 5 + i}}$$ can be expressed as
GATE CE 2014 Set 2
For an analytic function $$f\left( {x + i\,y} \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right),\,u$$ is given ...
GATE CE 2011
The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is
GATE CE 2010
The analytical function has singularities at, where $$f(z) = {{z - 1} \over {{z^2} + 1}}$$
GATE CE 2009
Potential function $$\phi $$ is given as $$\phi \, = \,{x^2}\, - \,{y^2}$$. What will be the stream function $$\psi $$ w...
GATE CE 2007
Which one of the following is not true for the complex number z1 and z2 ?
GATE CE 2005
$${e^z}$$ is a periodic with a period of
GATE CE 1997

Marks 2

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The value of the integral $$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3} ...
GATE CE 2009
Using Cauchy's Integral Theorem, the value of the integral (integration being taken in counter clockwise direction) $$\...
GATE CE 2006
Consider likely applicability of Cauchy's Integral theorem to evaluate the following integral counterclockwise around t...
GATE CE 2005

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