GATE EE

Complex Variable

Engineering Mathematics

(Past Years Questions)

Marks 1

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For a complex number $$z,$$ $$\mathop {Lim}\limits_{z \to i} {{{z^2} + 1} \over {{z^3} + 2z - i\left( {{z^2} + 2} \righ...
GATE EE 2017 Set 1
Consider the function $$f\left( z \right) = z + {z^ * }$$ where $$z$$ is a complex variable and $${z^ * }$$ denotes its...
GATE EE 2016 Set 2
Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ where $$f,g,h$$ are complex valued functions of a c...
GATE EE 2015 Set 2
Integration of the complex function $$f\left( z \right) = {{{z^2}} \over {{z^2} - 1}},$$ in the counterclockwise directi...
GATE EE 2014 Set 3
All the values of the multi valued complex function $${1^i},$$ where $$i = \sqrt { - 1} $$ are
GATE EE 2014 Set 2
Square roots of $$-i,$$ where $$i = \sqrt { - 1} $$ are
GATE EE 2013
Given $$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$$ wil...
GATE EE 2008

Marks 2

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The value of the contour integral in the complex - plane $$\oint {{{{z^3} - 2z + 3} \over {z - 2}}} dz$$ along the conto...
GATE EE 2017 Set 2
Consider the line integral $${\rm I} = \int\limits_c {\left( {{x^2} + i{y^2}} \right)dz,} $$ where $$z=x+iy.$$ The line ...
GATE EE 2017 Set 1
The value of the integral $$\oint\limits_c {{{2z + 5} \over {\left( {z - {1 \over 2}} \right)\left( {{z^2} - 4z + 5} \ri...
GATE EE 2016 Set 1
Let $$S$$ be the set of points in the complex plane corresponding to the unit circle. $$\left( {i.e.,\,\,S = \left\{ {z:...
GATE EE 2014 Set 1
$$\oint {{{{z^2} - 4} \over {{z^2} + 4}}} dz\,\,$$ evaluated anticlockwise around the circular $$\left| {z - i} \right| ...
GATE EE 2013
If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is
GATE EE 2012
Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-pl...
GATE EE 2012
A point $$z$$ has been plotted in the complex plane as shown in the figure below The plot of the complex number $$w =...
GATE EE 2011

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