Solution
= Solution
There are \b[<logarithmic branch points> at $z=-3i$ and infinity]. At zero, every local branch has $\log(3i)=\ln3+i(\pi/2+2\pi k)\ne0$, so division by $z^2$ gives \b[a <pole> of order two at zero]. Decay at infinity does not remove its branching: with $w=1/z$, the function is $w^2[\log(1+3iw)-\log w]$, which changes branch when $w$ encircles zero.