Multiplicative Group of Reals is Normal Subgroup of Complex

Theorem
Let $$\left({\mathbb{R}^*, \times}\right)$$ be the Multiplicative Group of Real Numbers.

Let $$\left({\mathbb{C}^*, \times}\right)$$ be the Multiplicative Group of Complex Numbers.

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