Additive Group of Reals is Normal Subgroup of Complex

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

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

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