Question about maximal ideals in a Polynomial ring

Question

I'm reading Freiligh and he has an example in a book, here it is:

Let $F = R$ and let $f(x) = x^2 + 1$. Which is well known to have no zeros in $R$ and thus is irreducible over $R$ by a theorem previously stated.

Then $<x^2+1>$ is a maximal ideal in $R[x]$. So $R[x]/<x^2 + 1>$ is a field.

This quotient ring is somehow isomorphic with the Complex numbers. I guess I'm having a hard time understanding why that is the case.

Being as simple as possible, can someone explain to me why that is the case. I don't know really advanced math.

Answer 1

Consider:

$\mathbb{R}[x] \rightarrow \mathbb{C}$, $f(x) \rightarrow f(i)$.