I don't understand why (1−i) is in the set of element of R2 in the solution.
My understanding is that Z/2Z={0,1}, endowed with addition and multiplication mod 2. So wouldn't the elements of R2 be {0,1,i,1+i}? And shouldn't the multiplication table of R2 be something like this?
Answer
Yes, you are right, the elements of R2 are 0, 1, i, and 1+i. And since, in Z/2Z, 1=−1, 1+i=1−i there.
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