Consider the subset Z[i] = {a + bi | a, b € Z} of the complex numbers, C. Note: Z[i] is called the set of Gaussian integers. a. Prove that Z[i] is a subring of C. b. Is Z[i] a commutative ring? Justify your answer. c. Is Z[i] a ring with identity? Justify your answer. d. Is Z[i] an integral domain? Prove or disprove. [Hint: C is an integral domain.] e. Is Z[i] a field? Prove or disprove. [Hint: The inverse of the complex number a + bi is 1 a-bi = :] a+bi a²+b²