[Math] Radius of convergence of power series of log z about a point

Question

I would like to determine the radius of convergence of the power series of log z expanded at -4+3i. I'm not sure how to tackle this – I've tried calculating the power series but I don't see what test or theorem I should use after that to find the radius of convergence. Can anyone point me in the right direction? Thanks!

Answer 1

There is a branch of $\log z$ holomorphic in $D(a,|a|)$, but not in $D(a,r)$ for any $r>|a|$. So basic complex analysis says the radius of convergence is $|a|$.