abstract algebra

Given:

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 31st roots of unity be represented with Euler’s formula:

cos(2πx / 31) + i sin(2πx / 31) = e^2πix/31

The function defined by f (e^2πix/31 ) = [x]31 is a homomorphism from G -> Z31

A. Prove that the given function is operation preserving.