Question

Evaluate 2) Zel/z? dz a) y=1171=5 Sol: Ti b) 8= 412+11-29 Sol: Ti

Answer 1

2) Szede let f(2)= Z²e 121 = 5} be the only Singularity in 12 = 5 n = Ž 1 (- 12) neo = 1-**-***** :: 732 1 = z²z+ ) 2! Z 31 Z3 4! Z5 Res ( f(2), 0) = coefficient of €) 2! 1 2 By Residue theorem , dz = 2011 * Res (f(a), o) 2:121= 5 S z² e = 2011 * Ž = ti

D={ 1Z+i)=2 12+i)=2) lZ+iſ=2 . Here o be the only Singularity in Iz+i)=2 2! so residue will unchange :: Res (f2), ) = By Residue theorem, Res (f(7),g) * 2771 8:12+71=2 그, 200 z3 e dz = s x 21 sti

D={ 1Z+i)=2 12+i)=2) lZ+iſ=2 . Here o be the only Singularity in Iz+i)=2 2! so residue will unchange :: Res (f2), ) = By Residue theorem, Res (f(7),g) * 2771 8:12+71=2 그, 200 z3 e dz = s x 21 sti
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