I am trying quiz questions of last year in Complex analysis by myself and I was unable to solve this particular problem .
Adding it's image:
I tried by putting z= 3$e^{it}$ and then changing limits from 0 to 2π but I am not able to simplify the integral so as to solve integral to get an answer.
Please help.
Do you know Residue Theorem. It is quite easy to evaluate the two sides using this theorem and you get the values of the two sides as $2 \pi i \lambda$ and $2 \pi i (-\frac 1 3)$. Hence (A) is the right answer.