I need help with a multiplication table for $\displaystyle Z_{2}[i] = {\{a+bi|a,b \in Z}\}$

I know the elements are {0, 1, i, i+1} for addition, are the multiplication elements the set \{0}?

Also, I can't figure out how to determine $\displaystyle i*i$ & $\displaystyle i(i+1)$

I have only had experience with modular arithmetic in $\displaystyle {Z}$

any explaination would be appreciated. Thanks in advance.