# Additive Group of Complex Numbers is Direct Product of Reals with Reals

## Theorem

Let $\struct {\C, +}$ be the additive group of complex numbers.

Let $\struct {\R, +}$ be the additive group of real numbers.

Then the direct product $\struct {\R, +} \times \struct {\R, +}$ is isomorphic with $\struct {\C, +}$.