Question: (Abstract Algebra - Rings and Subrings) Consider Z[i] := {a + bi | a, b Z} (the ring of Gaussian integers) a subring of C.

(Abstract Algebra - Rings and Subrings) Consider Z[i] := {a + bi | a, b Z} (the ring of Gaussian integers) a subring of C. (a) Find U(Z[i]) (Units of the Gaussian integers) (b) Is Z[i] a field? Is Z[i] an integral domain? Justify your answers.

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