Complex Variable · Engineering Mathematics · GATE ME

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Marks 1

GATE ME 2016 Set 3
Solutions of Laplace's equation having continuous second-order partial derivatives are called
GATE ME 2016 Set 1
$$f\left( z \right) = u\left( {x,y} \right) + i\,\,\,\,v\left( {x,y} \right)$$ is an analytic function of complex variable $$z=x+iy$$ , where $$i = \...
GATE ME 2015 Set 1
Given two complex numbers $${z_1} = 5 + \left( {5\sqrt 3 } \right)i$$ and $${z_2} = {2 \over {\sqrt 3 }} + 2i,$$ the argument of $${{{z_1}} \over {{z_...
GATE ME 2014 Set 2
An analytic function of a complex variable $$z=x+iy,$$ where $$i = \sqrt { - 1} $$ is expressed as $$f\left( z \right) = u\left( {x,y} \right) + i\,...
GATE ME 2014 Set 1
The argument of the complex number $${{1 + i} \over {1 - i}},$$ where $$i = \sqrt { - 1} ,$$ is
GATE ME 2011
The product of two complex numbers $$1 + i\,\,\,\,\& \,\,\,\,2 - 5\,i$$ is
GATE ME 2009
An analytic function of a complex variable $$z = x + i\,y$$ is expressed as $$f\left( z \right) = u\left( {x,y} \right) + i\,\,v\,\,\left( {x,y} \rig...
GATE ME 2008
The integral $$\oint {f(z)dz} $$ evaluated around the unit circle on the complex plane for $$f(z) = {{\cos z} \over z}$$ is
GATE ME 1996
$${i^i}$$, where $$i\, = \,\sqrt { - 1} $$ is given by

Marks 2

GATE ME 2017 Set 2
If $$f\left( z \right) = \left( {{x^2} + a{y^2}} \right) + ibxy$$ is a complex analytic function of $$z=x+iy,$$ where $${\rm I} = \sqrt { - 1} ,$$ th...
GATE ME 2016 Set 2
The value of $$\oint\limits_\Gamma {{{3z - 5} \over {\left( {z - 1} \right)\left( {z - 2} \right)}}dz} $$ along a closed path $$\Gamma $$ is equal to...
GATE ME 2016 Set 2
A function $$f$$ of the complex variable $$z=x+iy,$$ is given as $$f(x,y)=u(x,y)+iv(x,y),$$ Where $$u(x,y)=2kxy$$ and $$v(x,y)$$ $$ = {x^2} - {y^2}.$...
GATE ME 2016 Set 1
The value of the integral $$\int\limits_{ - \infty }^\infty {{{\sin x} \over {{x^2} + 2x + 2}}} dx$$ evaluated using contour integration and the res...
GATE ME 2014 Set 4
If $$z$$ is a complex variable, the value of $$\int\limits_5^{3i} {{{dz} \over z}} $$ is
GATE ME 2014 Set 3
An analytic function of a complex variable $$z = x + iy$$ is expressed as $$f\left( z \right) = u\left( {x + y} \right) + iv\left( {x,y} \right),$$ w...
GATE ME 2007
If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2nd derivatives then $$\phi (x,y)\, + \,i\psi (x,y)$$ can be expressed as an analyti...
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