Having real problems with a complex analysis homework. can the residue of a complex function at a simple pole be 0?
ie for g(z)= sin(z)/z i think the pole is just 0 of order one which is simple, but by calculating the residue i get 0..am i doing something wrong?
I'm using the formula if c is the simple pole and g(z)= f(z)/h(z) then the residue at c of g(z) = f(c)/h'(c)..is that okay?
Thanks for any help
So to make sure i have it right..
the function f(z)= 1/1+z^3 has a simple pole at z= -1. correct?
Then to get the residue at this pole can i use the formula res(f,c) where c is the simple pole = g(c)/h'(c) where g(c) is just 1, h'(z)= 3z^2 so h'(c)=3. so the residue is just 1/3? is that also correct?
Thank you for your patience!!