Additive Group of Reals is Normal Subgroup of Complex

Theorem
Let $$\left({\mathbb{R}, +}\right)$$ be the Additive Group of Real Numbers.

Let $$\left({\mathbb{C}, +}\right)$$ be the Additive Group of Complex Numbers.

Then $$\left({\mathbb{R}, +}\right)$$ is a normal subgroup of $$\left({\mathbb{C}, +}\right)$$.