Ring having no nilpotents Consider the ring $\mathbb{C}[x_1,\dots,x_n]/I$, where $I=(\sum_{i=1}^nx_i^2)$. I want to understand for what $n$ does this ring contain no nilpotents (i.e., for what $n$ is this algebra reduced).

I have no idea how to approach this problem. If $f+I$ is a nilpotent then $(f+I)^k=I$, but how to deduce the information about $n$ from here?..
the algebra $k[x_1,...,x_n]/I$ is reduced if and only if $I$ is a radical ideal. this from "Elementray algebraic geometry" Klaus Hulek, page 39
the algebra $k[x_1,...,x_n]/I$ is reduced if and only if $I$ is a radical ideal. this from "Elementray algebraic geometry" Klaus Hulek, page 39