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 ____.
Your input ____
2
GATE IN 2016
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+1
-0.3
Let $$j\, = \,\sqrt { - 1} $$. Then one value of $${j^j}$$ is
A
$$\sqrt 3 $$
B
-1
C
$${{\sqrt 3 } \over 2}$$
D
$${e^{ - {\pi \over 2}}}$$
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