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# G is the group of 31st roots of unity under complex multiplication. Z31 is the group of integers mod 31 under modular addition. Let elements in G be

G is the group of 31st roots of unity under complex multiplication. Z31 is the group of integers mod 31 under modular addition. Let elements in G be represented using exponential notation as ???? 2???????? 31 ???? where ???? is an integer ranging from 0 to 30. Consider the function defined by ???? (???? 2???????????? 31 ) = [????]31 from G -> Z31 . A. Prove that the given function is operation preserving