Dear @ll,
the central point (for the unitary gauge) in the higgs-mechanism is the equality
Φ = (v + η + iξ) = (v + η)ei(ξ/v) (see for example Halzen, Martin: Quarks and Leptons, eq. 14.56)
Φ = complex scalar Field
v = vacuum that breaks the symmetry spontaneously
η,ξ = shifted...