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## Marks 1

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

## Marks 2

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If $$f\left( z \right) = \left( {{x^2} + a{y^2}} \right) + ibxy$$ is a complex analytic function of $$z=x+iy,$$ where $... GATE ME 2017 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$...
GATE ME 2016 Set 2
The value of the integral $$\int\limits_{ - \infty }^\infty {{{\sin x} \over {{x^2} + 2x + 2}}} dx$$ evaluated using c...
GATE ME 2016 Set 1
The value of $$\oint\limits_\Gamma {{{3z - 5} \over {\left( {z - 1} \right)\left( {z - 2} \right)}}dz}$$ along a close...
GATE ME 2016 Set 2
If $$z$$ is a complex variable, the value of $$\int\limits_5^{3i} {{{dz} \over z}}$$ is
GATE ME 2014 Set 4
An analytic function of a complex variable $$z = x + iy$$ is expressed as $$f\left( z \right) = u\left( {x + y} \right)... GATE ME 2014 Set 3 If$$\phi (x,y)$$and$$\psi (x,y)$$are function with continuous 2nd derivatives then$$\phi (x,y)\, + \,i\psi (x,y) ...
GATE ME 2007

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