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?