# Complex Variables and Partial Differential Equations(3130005)

BE | Semester 3  Unit : Complex variable functions

## Q1 (a) Winter-2019   Find the real and imaginary parts of .

Unit : Complex variable functions

## Q1 (a) Summer-2020   Find the analytic function

Unit : Complex variable functions

## Q1 (b) Summer-2020   Find the roots of the equation, .

Unit : Complex variable functions

## Q1 (b) Winter-2019   State De-Movire’s formula and hence evaluate

Unit : Complex variable functions

## Q1 (c) Winter-2019   Define harmonic function. Show that  is a harmonic function. Find its harmonic conjugate $\mathrm{v}\left(\mathrm{x},\mathrm{y}\right)$.

Unit : Complex variable functions

## Q1 (c ( i )) Summer-2020   Determine & sketch the image of under the transformation .

Unit : Complex variable functions

## Q1 (c ( ii )) Summer-2020   Find the real and imaginary parts of .

Unit : Complex variable functions

## Q2 (a) Winter-2019   Determine the Mobius transformation which maps into .

Unit : Complex variable functions

## Q2 (b) Winter-2019   Define , prove that  .

Unit : Complex variable functions

## Q2 (b) Summer-2020   Determine the Mobius transformation which maps into .

Unit : Complex variable functions

## Q2 (c) Winter-2019   Find the image of the infinite strips under the transformation . Show the region graphically.

Unit : Complex variable functions

## Q3 (b) Winter-2019   Check whether the following functions are analytic or not at any point,

Unit : Complex variable functions

## Q2 (c( i )) Summer-2020   Find the fourth roots of -1.

Unit : Complex variable functions

## Q2 (c ( ii )) Summer-2020   Find the roots of .

Unit : Complex variable functions

## Q3 (b) Winter-2019   If  , is an analytic function,prove that  .

Unit : Complex variable functions