1. Prove or disprove that the given set is a subgroup of the given group G. (a) H = {a + bi|a,b e R, a² + b² = 1}; G = C* under multiplication (b) H = {|" a + b+ c +d = :G = {a la, b, c, b E Z under matrix addition .C b dl by (c) H = {|" a + b + c+ d = 1};G = (d) Let r ands be positive integers, H = {nr + ms|m,n E Z}; G = Z under the usual addition of integers. (e) H = {a + bila,b e R, ab > 0}; G = C under addition {I. la, b, c, b E Z} under matrix addition

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