Disc of convergence

Question

I just worked out the disc of convergence of $$\sum_{n=0}^{\infty} \frac{(3-i)^n}{n^2}(z+2)^n$$ using the ratio test and I just wanted to check if other people would get the same result.

I got it is convergent in $|z+2|<\frac{3}{10}+\frac{i}{10}$ is this what other people get?

(z is a complex number $i=\sqrt{-1}$)

Answer 1

By Cauchy-Hadamard:

$$\frac1R=\limsup_{n\to\infty}\sqrt[n]{\frac{|3-i|^n}{n^2}}=|3-i|=\sqrt{10}$$