1
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral $${1 \over {2\pi j}}\oint\limits_C {{{{e^z}} \over {z - 2}}dz} $$ along a closed contour $$c$$ in anti-clockwise direction for
(i) the point $${z_0} = 2$$ inside the contour $$c,$$ and
(ii) the point $${z_0} = 2$$ outside the contour $$c,$$ respectively, are
A
(i) $$2.72,$$ (ii) $$0$$
B
(i) $$7.39,$$ (ii) $$0$$
C
(i) $$0,$$ (ii) $$2.72$$
D
(i) $$0,$$ (ii) $$7.39$$
2
GATE ECE 2016 Set 2
Numerical
+2
-0
Consider the complex valued function $$f\left( z \right) = 2{z^3} + b{\left| z \right|^3}$$ where $$z$$ is a complex variable. The value of $$b$$ for which the function $$f(z)$$ is analytic is __________.
Your input ____
3
GATE ECE 2016 Set 1
Numerical
+2
-0
In the following integral, the contour $$C$$ encloses the points $${2\pi j}$$ and $$-{2\pi j}$$. The value of the integral $$ - {1 \over {2\pi }}\oint\limits_c {{{\sin z} \over {{{\left( {z - 2\pi j} \right)}^3}}}} dz$$ is ___________.
Your input ____
4
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
$$2\pi n$$
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