1
GATE IN 2016
Numerical
+1
-0
The value of the integral $${1 \over {2\pi j}}\int\limits_c {{{{z^2} + 1} \over {{z^2} - 1}}} dz$$
where $$z$$ is a complex number and $$C$$ is a unit circle with center at $$1+0j$$ in the complex plane is ____.
2
GATE IN 2016
+1
-0.3
In the neighborhood of $$z=1,$$ the function $$f(z)$$ has a power series expansion of the form
$$f\left( z \right) = 1 + \left( {1 - z} \right) + {\left( {1 - z} \right)^2} + ..................$$
Then $$f(z)$$ is
A
$${1 \over z}$$
B
$${{ - 1} \over {z - 2}}$$
C
$${{z - 1} \over {z + 1}}$$
D
$${1 \over {2z - 1}}$$
3
GATE IN 2015
+1
-0.3
The value of $$\oint\limits_c {{1 \over {{z^2}}}dz}$$ where the contour is the unit circle traversed clock - wise, is
A
$$- 2\pi i$$
B
$$0$$
C
$$2\pi i$$
D
$$4\pi i$$
4
GATE IN 2007
+1
-0.3
For the function $${{\sin z} \over {{z^3}}}$$ of a complex variable z, the point z = 0 is
A
a pole of order 3
B
a pole of order 2
C
a pole of order 1
D
not a singularity
GATE IN Subjects
Engineering Mathematics
EXAM MAP
Joint Entrance Examination