1
GATE ME 2009
MCQ (Single Correct Answer)
+1
-0.3
An analytic function of a complex variable $$z = x + i\,y$$ is expressed as
$$f\left( z \right) = u\left( {x,y} \right) + i\,\,v\,\,\left( {x,y} \right)$$ where $$i = \sqrt { - 1} .$$
If $$u=xy$$ then the expression for $$v$$ should be
A
$${{{{\left( {x + y} \right)}^2}} \over 2} + k$$
B
$${{x - {y^2}} \over 2} + k$$
C
$${{{y^2} - {x^2}} \over 2} + k$$
D
$${{{{\left( {x - y} \right)}^2}} \over 2} + k$$
2
GATE ME 2008
MCQ (Single Correct Answer)
+1
-0.3
The integral $$\oint {f(z)dz} $$ evaluated around the unit circle on the complex plane for $$f(z) = {{\cos z} \over z}$$ is
A
$$2\pi i$$
B
$$4\pi i$$
C
$$-2\pi i$$
D
0
3
GATE ME 1996
MCQ (Single Correct Answer)
+1
-0.3
$${i^i}$$, where $$i\, = \,\sqrt { - 1} $$ is given by
A
0
B
$${e^{ - {\pi \over 2}}}$$
C
$${\pi \over 2}$$
D
1
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Turbo Machinery
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