1. The problem statement, all variables and given/known data Hi all, I posted the image of the solution here. My questions concerns the evaluation of the Residue at z=i. 2. Relevant equations None needed, all giving in the question -- simple algebraic mistake made is likely to be the problem here. 3. The attempt at a solution We see that phi function is clearly equal to 1/(z+i)^2 as the show. Since it is a pole of order two, we must differentiate this function first before evaluation at singular point i. The derivative of this function should be -2/(z+i)^(3) Now we can evaluate this at point z=i. -2/(2i)^3 = -2/8i^3 = -1/4i^3. When I calculate this, this becomes i/4 But the answer states that this is instead 1/4i. Where am I going wrong in my complex algebra?