The exact Green's functions of a Luttinger Liquid (LL) connected to impedances are computed at zero and finite temperature. It is also shown that if the resistances are equal to the characteristic impedance of the Luttinger liquid, then the finite Luttinger liquid connected to resistors is equivalent to an infinite Luttinger liquid. Impedance boundary conditions (IBC) include also as a special limit the case of open boundary conditions, which are explicitly recovered. Finally bosonization for a LL with IBC is proven to hold.