## 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\, = \,\...