1
GATE ECE 2022
Numerical
+1
-0

A simple closed path C in the complex plane is shown in the figure. If

$$\oint\limits_c {{{{2^z}} \over {{z^2} - 1}}dz = - i\pi A} $$,

where $$i = \sqrt { - 1} $$, then the value of A is ___________ (rounded off to two decimal places).

GATE ECE 2022 Engineering Mathematics - Complex Variable Question 3 English

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2
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are
A
$${{ - 1} \over {27}}$$ and $${{ - 1} \over {125}}$$
B
$${1 \over {125}}$$ and $${{ - 1} \over {125}}$$
C
$${{ - 1} \over {27}}$$ and $${1 \over 5}$$
D
$${1 \over {125}}$$ and $${{ - 1} \over 5}$$
3
GATE ECE 2016 Set 3
Numerical
+1
-0
For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.
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4
GATE ECE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The imaginary part of $$f(z)$$ is
A
$${e^y}\cos \left( x \right)$$
B
$${e^{ - y}}sin\left( x \right)$$
C
$$ - {e^y}sin\left( x \right)$$
D
$$ - {e^{ - y}}sin\left( x \right)$$
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