Complex Variables and Partial Differential Equations (3130005)

BE | Semester-3   Summer-2020 | 27-10-2020

Q3) (b)

For, fz = 1 z-12z-3 , find the residue at z = 1.

fz = 1 z-12z-3 
 
Resfz,z0 = 1 n-1 !  limzz0 dn-1dzn-1z-z0n fz
 
Resfz,1 = 1 1 !  limz1 d1dz1z-12 1 z-12z-3 
 
Resfz,1 = limz1 - 1 z-32 
 
Resfz,1 = - 1 4