1
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
$$4\pi \left( {1 - j2} \right)$$
2
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
$$1$$
3
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
$${1 \over 2},\,\, - 1,\,\,{3 \over 2}$$
4
GATE ECE 2009
+1
-0.3
If $$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$ then $$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}} \,\,dz$$ is given
A
$$2\,\pi \,{C_1}$$
B
$$2\,\pi \,(1 + {C_0})$$
C
$$2\,\pi \,j\,{C_1}$$
D
$$2\,\pi \,j\,(1 + {C_0})$$
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