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I'm struggling to see what the structure of a quotient ring such as

$$\mathbb Z[i] / (1+i)$$ is. I think it's supposed to be isomorphic to $\mathbb Z / 2\mathbb Z$ but I don't see how.

Can someone give me a hand?

IAlreadyHaveAKey
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    Have you tried to draw a diagram showing the Gaussian integers with those in the ideal $(1+i)$ highlighted? You should be able to see on it that every element is either in the ideal or just to the right of something that is in the ideal. – hmakholm left over Monica May 16 '16 at 11:12

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Hint: $\mathbb Z[i]$ is an Euclidean ring and $N(1+i)=2$.

lhf
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