1
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
$$- {e^{ - y}}sin\left( x \right)$$
2
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
$$4\pi \left( {1 - j2} \right)$$
3
GATE ECE 2011
+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
$$1$$
4
GATE ECE 2010
+1
-0.3
The residues of a complex function $$X\left( z \right) = {{1 - 2z} \over {z\left( {z - 1} \right)\left( {z - 2} \right)}}$$ at it poles
A
$${1 \over 2},\,\, - {1 \over 2},\,1$$
B
$${1 \over 2},\,\, - {1 \over 2},\, - 1$$
C
$${1 \over 2},\,\,1,\,\, - {3 \over 2}$$
D
$${1 \over 2},\,\, - 1,\,\,{3 \over 2}$$
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