Homomorphism_from_Reals_to_Circle_Group_v2

Let $\struct {\R, +}$ be the additive group of real numbers. Let $\struct {K, \times}$ be the circle group. Let $\phi: \struct {\R, +} \to \struct {K, \times}$ be the mapping defined as $\forall x \in \R: \map \phi x = e^{i x}$ Then $\phi$ is a (group) homomorphism.