Q: Determine U(Z[i]) ?
My book solves this by taking some unit a+bi of Z[i], and then multiplying it with its multiplicative inverse say, c+di.
=> (a+bi)(c+di) = 1
Taking modulus on both sides
=> (a2+b2)(c2+d2) = 1
=> a2+b2= 1, I don't really understand this step. Can someone please tell me how my book arrived to this conclusion ?