I don't understand correct answer of one example.
There is defined set $Z[i] = \{a+bi | a,b \in \mathbb{Z}\}$ and I need to find characteristic of quotient ring $Z[i]/(2+2i)$. What is the correct answer? I found that is 4, and I don't understand why. According to definition I thought that it is 0, but it isn't. I also read some questions on this site, but i am still note sure. Could someone help me?
Next question is to find all elements of mentioned quotient ring. I have these: 1,-1,i,-i,1+i,1-i,-1+i,-1-i. Is it correct?
In that ring $$1+1+1+1=4=(2+2i)(1-i)=0$$