Exercise

Consider the Gaussian numbers R = Q + Qi (a variation of the Gaussian integers), with the usual multiplication (i² = -1) and addition. What are the invertible elements of R?

{1, -1}

{1,-1, i, -i}

{1,-1, i, -i, (1+i)/2, (1-i)/2, (-1+i)/2, (-1-i)/2}

R\{0}