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Consider the following complex function $$f\left( z \right) = {9 \over {\left( {z - 1} \right)\left( {z + 2} \right)}}.... GATE CE 2015 Set 1$$z = {{2 - 3i} \over { - 5 + i}}$$can be expressed as GATE CE 2014 Set 2 For an analytic function$$f\left( {x + i\,y} \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right),\,u$$is given ... GATE CE 2011 The modulus of the complex number$${{3 + 4\,i} \over {1 - 2\,i}}$$is GATE CE 2010 The analytical function has singularities at, where$$f(z) = {{z - 1} \over {{z^2} + 1}}$$GATE CE 2009 Potential function$$\phi $$is given as$$\phi \, = \,{x^2}\, - \,{y^2}$$. What will be the stream function$$\psi $$w... GATE CE 2007 Which one of the following is not true for the complex number z1 and z2 ? GATE CE 2005$${e^z}$$is a periodic with a period of GATE CE 1997 ## Marks 2 More The value of the integral$$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3} ...
GATE CE 2009
Using Cauchy's Integral Theorem, the value of the integral (integration being taken in counter clockwise direction) \...
GATE CE 2006
Consider likely applicability of Cauchy's Integral theorem to evaluate the following integral counterclockwise around t...
GATE CE 2005

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