1
GATE ME 2016 Set 2
Numerical
+2
-0
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 $$v(x,y)$$ $$ = {x^2} - {y^2}.$$
The value of $$k,$$ for which the function is analytic, is __________.
Your input ____
2
GATE ME 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $$\int\limits_{ - \infty }^\infty {{{\sin x} \over {{x^2} + 2x + 2}}} dx$$
evaluated using contour integration and the residue theorem is
A
$$ - \pi {{\sin \left( 1 \right)} \over e}$$
B
$$ - \pi {{\cos \left( 1 \right)} \over e}$$
C
$${{\sin \left( 1 \right)} \over e}$$
D
$${{\cos \left( 1 \right)} \over e}$$
3
GATE ME 2014 Set 4
MCQ (Single Correct Answer)
+2
-0.6
If $$z$$ is a complex variable, the value of $$\int\limits_5^{3i} {{{dz} \over z}} $$ is
A
$$ - 0.511 - 1.57i$$
B
$$-0.511+1.57i$$
C
$$0.511-1.57i$$
D
$$0.511+1.57i$$
4
GATE ME 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
An analytic function of a complex variable $$z = x + iy$$ is expressed as
$$f\left( z \right) = u\left( {x + y} \right) + iv\left( {x,y} \right),$$ where $$i = \sqrt { - 1} .$$ If $$u(x, y)=$$ $${x^3} - {y^2}$$
then expression for $$v(x,y)$$ in terms of $$x,y$$ and a general constant $$c$$ would be
A
$$xy+c$$
B
$${{{x^2} + {y^2}} \over 2} + c$$
C
$$2xy+c$$
D
$${{{{\left( {x - y} \right)}^2}} \over 2} + c$$
GATE ME Subjects
Turbo Machinery
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
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CBSE
Class 12