Find the points where the function  is not analytic. 

Find the image of the circle under the mapping  What happens when r = 1 ?

22-1 Prove that the linear fractional transformation maps the circle  into itself. Also prove that  is conformal in 

Find the maximum modulus  on the closed circular region defined by

Find the radius of convergence of the following series.

i)   ii)        

Consider  and the closed circular region  Find points in R where |  | has its maximum and minimum values.

Find all the singularities of the function