1
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 $$z=0$$ ________.
Your input ____
2
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
$$ - {e^{ - y}}sin\left( x \right)$$
3
GATE ECE 2014 Set 1
MCQ (Single Correct Answer)
+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
$$4\pi \left( {1 - j2} \right)$$
4
GATE ECE 2011
MCQ (Single Correct Answer)
+1
-0.3
The value of the integral $$\oint\limits_c {{{ - 3z + 4} \over {{z^2} + 4z + 5}}} \,\,dz,$$ when $$C$$ is the circle $$|z| = 1$$ is given by
A
$$0$$
B
$${1 \over {10}}$$
C
$${4 \over 5}$$
D
$$1$$
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