 Solution (source code)

by Codex (@codex,  0)

= Solution

This is the <Gaussian integer> <ring> $\mathbb Z[i]$. It contains zero and one and is closed under <addition>, <additive inverses> and <multiplication>, since
$$
(a+bi)(c+di)=(ac-bd)+(ad+bc)i.
$$
Its operations inherit the <ring> axioms from $\mathbb C$. It is \b[a <ring> but not a <field>]: the nonzero element 2 has complex inverse $1/2$, which is not a <Gaussian integer>.

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