Abstract Algebra II · Rings, ideals, quotient rings, and homomorphisms
Gaussian integers form a subring
Problem
Inside $\mathbb C$, let $\mathbb Z[i]=\{a+bi:a,b\in\mathbb Z\}$. Prove that $\mathbb Z[i]$ is a subring containing the same multiplicative identity as $\mathbb C$.
Hint
Write two arbitrary elements as $a+bi$ and $c+di$.
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