Show $\mathbb{C}\backslash \left\{ -1 \right\}$ can be seen $\mathbb{R}$ linear space with the addition $a\oplus b=a+b+ab$

Question

Let $V=\mathbb{C}\backslash \left\{-1\right\}$ and define the special addition $\oplus$ on $V$, for $\forall a,b\in V$ $$a\oplus b=a+b+ab.$$

Then we can check that $V$ satisfies all additive conditions in linear space with the special addition $\oplus$.

For example, the zero element is $0$, the additive inverse element of $a$ is $\dfrac{-a}{a+1}$.

My question is how can I define the scalar multiplication on $V$ so that $V$ can be seen as a $\mathbb{C}-$ linear space?

Any help and references are greatly appreciated.

Thanks!