Radius of convergence of the power series, obtained by the Taylor expansion of $f(z) = \frac{(z+20)(z+21)}{(z-20i)^{21} (z^2 +z+1)}$ about $z = 0$. Write down the radius of convergence of the power series, obtained by the Taylor expansion of the analytic functions about the stated point, in
$f(z) = \frac{(z+20)(z+21)}{(z-20i)^{21} (z^2 +z+1)}$ about $z = 0$.
My attempt: Since power series are continuous on the disk of convergence, the radius of convergence is the distance to the nearest point of discontinuity. $f(z)$ is not analytic at $z=20i$, hence the radius of convergence would be $|0-20i|= \sqrt{20}$.
Am I correct?

The radius of convergence is the distance from $0$ to the nearest singularity. And the nearest singularities are $-\frac12\pm\frac{\sqrt3}2i$ (the roots of $z^2+z+1$), whose distance to $0$ is $1$.
