1
GATE EE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
All the values of the multi valued complex function $${1^i},$$ where $$i = \sqrt { - 1} $$ are
A
purely imaginary
B
real and non negative
C
on the unit circle
D
equal in real and imaginary parts.
2
GATE EE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Integration of the complex function $$f\left( z \right) = {{{z^2}} \over {{z^2} - 1}},$$ in the counterclockwise direction, around $$\left| {z - 1} \right| = 1,$$ is
A
$$ - \pi i$$
B
$$0$$
C
$$\pi i$$
D
$$2\pi i$$
3
GATE EE 2013
MCQ (Single Correct Answer)
+1
-0.3
Square roots of $$-i,$$ where $$i = \sqrt { - 1} $$ are
A
$$i, -i$$
B
$$\eqalign{ & \cos \left( { - {\pi \over 4}} \right) + \sin \left( { - {\pi \over 4}} \right), \cr & \cos \left( {{{3\pi } \over 4}} \right) + i\,\sin \left( {{{3\pi } \over 4}} \right) \cr} $$
C
$$\eqalign{ & \cos \left( {{\pi \over 4}} \right) + i\sin \left( {{{3\pi } \over 4}} \right), \cr & \cos \left( {{{3\pi } \over 4}} \right) + i\sin \left( {{\pi \over 4}} \right) \cr} $$
D
$$\eqalign{ & \cos \left( {{{3\pi } \over 4}} \right) + i\sin \left( { - {{3\pi } \over 4}} \right), \cr & \cos \left( { - {{3\pi } \over 4}} \right) + i\sin \left( {{{3\pi } \over 4}} \right) \cr} $$
4
GATE EE 2008
MCQ (Single Correct Answer)
+1
-0.3
Given $$X(z) = {z \over {{{(z - a)}^2}}}$$ with |z| > a, the residue of $$X(z){z^{n - 1}}$$ at z = a for $$n \ge 0$$ will be
A
an - 1
B
an
C
nan
D
nan - 1
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