1
GATE ME 2017 Set 2
+2
-0.6
If $$f\left( z \right) = \left( {{x^2} + a{y^2}} \right) + ibxy$$ is a complex analytic function of $$z=x+iy,$$
where $${\rm I} = \sqrt { - 1} ,$$ then
A
$$a=-1,b=-1$$
B
$$a=-1, b=2$$
C
$$a=1, b=2$$
D
$$a=2, b=2$$
2
GATE ME 2016 Set 2
+2
-0.6
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 $$\left( {4\pi i} \right),$$ where $$z=x+iy$$ and $$i = \sqrt { - 1} .$$ The correct path $$\Gamma$$ is
A
B
C
D
3
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 __________.
4
GATE ME 2016 Set 1
+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
$${{\cos \left( 1 \right)} \over e}$$
GATE ME Subjects
EXAM MAP
Medical
NEET