Thread: residue

find the residue of exp (iaz) / (cosh (pi z))^2 at z= i/2.

what i did was to differentiate exp (iaz) at z= i/2 but the answer seems to say that i need to differentiate
exp (iaz) / (cosh (pi z))^2.

may i know why?

I would actually say "neither". It looks like you have a second-order pole at the point of interest, in which case you should do this. Make sense?