4)Find the Laurent series expansion of the function 2z/ z²+2z-3 in the region 2<|z+1| <4.
Explain the problem with step by step process?
The Taylor series is the Laurent expansion about z = 0 because the function is analytic there and has radius of convergence 1.
The expansions about i and -i have one term with a power -1. As z^2 + 1 = (z-i)(z+i) you can multiply your function by one of the factors, find the Taylor series, then divide all terms by that factor. And voila! there’s a Laurent series.