Monolithic Groups

Question

I have recently gone through the semi-direct product of groups. While I was studying monolithic groups (a group is said to be monolithic if it has a unique minimal normal subgroup, and this is contained in every nontrivial normal subgroup), I saw the following: let $F$ be a field and let $F^{+}$ and $F^{\ast}$ denote the additive and multiplicative group of $F$. The semidirect product $G = F^{+} \rtimes F^{\ast}$, with the action of $F^{\ast}$ on $F^{+}$ by multiplication, contains a unique minimal normal subgroup $F^{+}$. It seems that $G$ is a monolithic group, but I can not see why. I am completely stuck, please help me.