Question

Determine the residue of a. 2x+3/z^2-4 b. z-3/z^3+5z^2

Answer 1

The residue at 0 of (2z+3)/z²-4=2/z+3/z²-4 is 2 since it is equal to the coefficient a_-1 in Laurent expansion around 0.

Analogously, the residue of (z-3)/z³+5z²=1/z²-3/z³+5z² at 0 is 0 since the coefficient $a_{-1}$ in the Laurent expansion around 0 is 0.