For the power series $\sum a_n z^n$ with $a_n = (3+4i)^n$, the radius of convergence is $R = \dfrac{1}{\limsup|a_n|^{1/n}} = \dfrac{1}{|3+4i|} = \dfrac{1}{\sqrt{9+16}} = \dfrac{1}{\sqrt{25}} = \dfrac{1}{5}$.