GATE CE
Engineering Mathematics
Complex Variable
Previous Years Questions

## Marks 1

Consider the following complex function $$f\left( z \right) = {9 \over {\left( {z - 1} \right)\left( {z + 2} \right)}}.$$ Which of the following is O...
$$z = {{2 - 3i} \over { - 5 + i}}$$ can be expressed as
For an analytic function $$f\left( {x + i\,y} \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right),\,u$$ is given by $$u = 3{x^2} - 3{y^2}.$$ Th...
The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is
The analytical function has singularities at, where $$f(z) = {{z - 1} \over {{z^2} + 1}}$$
Potential function $$\phi$$ is given as $$\phi \, = \,{x^2}\, - \,{y^2}$$. What will be the stream function $$\psi$$ with the condition $$\psi \, = ... Which one of the following is not true for the complex number z1 and z2 ?$${e^z}$$is a periodic with a period of ## Marks 2 The value of the integral$$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3} \right)}}} dz$$where C is a c... Using Cauchy's Integral Theorem, the value of the integral (integration being taken in counter clockwise direction)$$\int\limits_C {{{{z^3} - 6} \ov...
Consider likely applicability of Cauchy's Integral theorem to evaluate the following integral counterclockwise around the unit circle C. I\, = \,\...
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