Q: Proof of an algebraic expression I've an expression $\displaystyle \Bbb Z[i]/\langle1+3i\rangle \cong \frac{\Bbb Z[x]/\langle x^2+1\rangle}{\langle1+3x,x^2+1\rangle/\langle x^2+1\rangle}$. 
I am unable to understand how it comes. I know that $\displaystyle \Bbb Z[i]\cong \Bbb Z[x]/\langle x^2+1\rangle$. But what about the denominator ?
