1
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If $$C$$ is a circle of radius $$r$$ with centre $${z_0}$$ in the complex $$z$$-plane and if $$'n'$$ is a non-zero integer, then $$\oint\limits_c {{{dz} \over {{{\left( {z - {z_0}} \right)}^{n + 1}}}}} $$ equals
A
$$2\pi nj$$
B
$$0$$
C
$${{nj} \over {2\pi }}$$
D
$$2\pi n$$
2
GATE ECE 2015 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$z=x+iy$$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction . Which one of the following statement is NOT TRUE?
A
The residue of $${z \over {{z^2} - 1}}$$ at $$z=1$$ is $${1 \over 2}$$
B
$$\oint\limits_C {{z^2}\,\,dz = 0} $$
C
$${1 \over {2\pi i}}\oint\limits_c {{1 \over z}} dz = 1$$
D
$$\overline z $$ (complex conjugate of $$z$$ ) is an analytical function.
3
GATE ECE 2012
MCQ (Single Correct Answer)
+2
-0.6
If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is
A
$${e^{ - \pi /2}}$$
B
$${e^{ \pi /2}}$$
C
$$x$$
D
$$1$$
4
GATE ECE 2012
MCQ (Single Correct Answer)
+2
-0.6
Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-plane such that
$$\left| {z + 1} \right| = 1,$$ the value of $${1 \over {2\,\pi \,j}}\oint\limits_c {f\left( z \right)dz} $$ is
A
$$-2$$
B
$$-1$$
C
$$1$$
D
$$2$$
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