## Marks 1

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The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are
GATE ECE 2017 Set 2
For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.
GATE ECE 2016 Set 3
The real part of an analytic function $$f(z)$$ where $$z=x+jy$$ is given by $${e^{ - y}}\cos \left( x \right).$$ The ima...
GATE ECE 2014 Set 2
$$C$$ is a closed path in the $$z-$$plane given by $$\left| z \right| = 3.$$ The value of the integral $$\oint\limits_... GATE ECE 2014 Set 1 The value of the integral$$\oint\limits_c {{{ - 3z + 4} \over {{z^2} + 4z + 5}}} \,\,dz,$$when$$C$$is the circle$$|...
GATE ECE 2011
The residues of a complex function $$X\left( z \right) = {{1 - 2z} \over {z\left( {z - 1} \right)\left( {z - 2} \right)}... GATE ECE 2010 If$$f\left( z \right) = {C_0} + {C_1}{z^{ - 1}}\,\,$$then$$\oint\limits_{|z| = 1} {{{1 + f\left( z \right)} \over z}}...
GATE ECE 2009
The residue of the function $$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$ at z = 2 is...
GATE ECE 2008
The equation sin(z) = 10 has
GATE ECE 2008
The value of $$\oint\limits_C {{1 \over {\left( {1 + {z^2}} \right)}}} dz$$ where C is the contour $$\,\left| {z - {i \o... GATE ECE 2007 The value of the counter integral$$$\int\limits_{\left| {z - j} \right| = 2} {{1 \over {{z^2} + 4}}\,} dz\,\,in\,the\,p... GATE ECE 2006 For the function of a complex variable w = lnz (where w = u + jv and z = x + jy) the u = constant lines get mapped in th... GATE ECE 2006 ## Marks 2 More The contour C given below is on the complex plane $$z = x + jy$$, where $$j = \sqrt { - 1}$$. The value of the integra... GATE ECE 2018 An integral $${\rm I}$$ over a counter clock wise circle $$C$$ is given by $${\rm I} = \oint\limits_c {{{{z^2} - 1} \ove... GATE ECE 2017 Set 2 The value of the integral$${1 \over {2\pi j}}\oint\limits_C {{{{e^z}} \over {z - 2}}dz} $$along a closed contour$$c$$... GATE ECE 2016 Set 3 Consider the complex valued function$$f\left( z \right) = 2{z^3} + b{\left| z \right|^3}$$where$$z$$is a complex va... GATE ECE 2016 Set 2 In the following integral, the contour$$C$$encloses the points$${2\pi j}$$and$$-{2\pi j}$$. The value of the integr... GATE ECE 2016 Set 1 If$$C$$is a circle of radius$$r$$with centre$${z_0}$$in the complex$$z$$-plane and if$$'n'$$is a non-zero integ... GATE ECE 2015 Set 3 Let$$f\left( z \right) = {{az + b} \over {cz + d}}.$$If$$f\left( {{z_1}} \right) = f\left( {{z_2}} \right)$$for all ... GATE ECE 2015 Set 2 If$$C$$denotes the counter clockwise unit circle. The value of the contour integral$${1 \over {2\pi i}}\oint\limits_c... GATE ECE 2015 Set 2 Let $$z=x+iy$$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockw... GATE ECE 2015 Set 1 If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is GATE ECE 2012 Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-pl... GATE ECE 2012 If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral$\$\oint\limits_D {{...
GATE ECE 2007

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