PILL Consider the sub-ring EH 5] := {a + h 1...? 5 | a. b E E} of field C of complex numbers {i} Show that the norm function N: Eh? 5] z- E def'med h? N{a + b 1.! 5) = a3 + 5 b3 is compatible with multiplication. meaning that the norm of a product is equal to the product of the norms of the factors. [ii] Confirm that 2 + w...\" 5 is an irreducible element in EH 5]. {iii} Verify that the ideal {2 + 1.," 5} is not prime in EH 5]