Which of the following correctly describes the set of Gaussian integers Z[i]\mathbb{Z}[i]Z[i]?
Z[i]={a+bi∣a,b∈Z}\mathbb{Z}[i] = \{a + bi \mid a, b \in \mathbb{Z}\}Z[i]={a+bi∣a,b∈Z} forms a field
Z[i]={a+bi∣a,b∈Z}\mathbb{Z}[i] = \{a + bi \mid a, b \in \mathbb{Z}\}Z[i]={a+bi∣a,b∈Z} forms a ring but not a field
Z[i]\mathbb{Z}[i]Z[i] contains only real numbers
Z[i]\mathbb{Z}[i]Z[i] is not closed under addition