Find residuum f(z)=sin(z) / (e^z^2-1) + sin(jz / (z - 1)) in pionts z=0, z=1?

Question

z is a complex number, z=x+jy= a+bi

Answer 1

Unless j=0, I believe the singularity at z=1 is essential.  There may be an analog to the residue for essential singularities, but I don't know it.

As for the singularity at z=0, it's obvious when you write the series for the sine and the exponential that it has a simple pole.

Res(z=0)f(z) = lim(z->0) (zsin(z) / (e^(z^2) - 1) + zsin(jz / (z-1)))

= 1