1
GATE ECE 2017 Set 2
+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 $${{ - 1} \over 5}$$
2
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 $$z=0$$ ________.
3
GATE ECE 2014 Set 2
+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
$$- {e^{ - y}}sin\left( x \right)$$
4
GATE ECE 2014 Set 1
+1
-0.3
$$C$$ is a closed path in the $$z-$$plane given by
$$\left| z \right| = 3.$$ The value of the integral
$$\oint\limits_c {{{{z^2} - z + 4j} \over {z + 2j}}dz}$$ is
A
$$- 4\pi \left( {1 + j2} \right)$$
B
$$4\pi \left( {3 - j2} \right)$$
C
$$- 4\pi \left( {3 + j2} \right)$$
D
$$4\pi \left( {1 - j2} \right)$$
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