1
GATE ECE 2008
+1
-0.3
The residue of the function
$$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$ at z = 2 is
A
$$- {1 \over {32}}$$
B
$$- {1 \over {16}}$$
C
$${1 \over {16}}$$
D
$${1 \over {32}}$$
2
GATE ECE 2007
+1
-0.3
The value of $$\oint\limits_C {{1 \over {\left( {1 + {z^2}} \right)}}} dz$$ where C is the contour $$\,\left| {z - {i \over 2}} \right| = 1$$ is
A
$$2\pi i$$
B
$$\pi$$
C
$${\tan ^{ - 1}}(z)$$
D
$$\pi i{\tan ^{ - 1}}(z)$$
3
GATE ECE 2006
+1
-0.3
The value of the counter integral $$\int\limits_{\left| {z - j} \right| = 2} {{1 \over {{z^2} + 4}}\,} dz\,\,in\,the\,positive\,sense\,is$$\$
A
$${{j\pi } \over 2}$$
B
$${{ - \pi } \over 2}$$
C
$${{ - j\pi } \over 2}$$
D
$${\pi \over 2}$$
4
GATE ECE 2006
+1
-0.3
For the function of a complex variable w = lnz (where w = u + jv and z = x + jy) the u = constant lines get mapped in the z-plane as
A
B
set of concentric circles
C
set of confocal hyperbola
D
set of confocal ellipses
EXAM MAP
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