# Why does Higgs field have 4 components and written in a doublet?

I'm studying the Higgs field and I encountered some problems. My book says that the Higgs field has four components which are conveniently arranged into a two-component vector as: $$\phi=\binom{\phi^{+}}{\phi^{0}}=\frac{1}{\sqrt{2}} \binom{\phi_{3}+i\phi_{4}}{\phi_{1}+i\phi_{2}}$$ My question is that why does Higgs field have 4 components? If it has 4 components, why don't we just write it like: $$\phi=\begin{pmatrix} \phi_{3}\\ \phi_{4}\\ \phi_{1}\\ \phi_{2} \end{pmatrix}$$ A more genral problem I've been having is that how do I know if something can be written in a multiplet and what kind of multiplet should I use to represent a state?

• So how do I know that the Higgs field is invariant under $SU(2)$?