Residue Calculus for Evaluating e^z/cosh z on Circle |z|=5

[David Laz]

I need to use residue calculus to evaluate:
\oint_C {\frac{{e^z }}{{\cosh z}}} dz
where C is the circle |z|=5
My only problem (which is a stupid one) is working out how many poles the function has inside the circle. I know its going to have them at pi*i/2 + pi*i*k. This is probably a really stupid question, but I've left a lot of this course till the last minute. :(

 

[David Laz]

Worked it out. I'm an idiot for overlooking something so simple.