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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$$wil... GATE EE 2008 Marks 2 More The value of the contour integral in the complex - plane$$\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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