Equations for formally real meadows

We consider the signatures ${\mathrm{\Sigma }}_m=(0,1,-,+,\cdot ,{}^{-1})$ of meadows and $({\mathrm{\Sigma }}_m,\mathbf{s})$ of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom scheme expressing formal realness; the second axiomatization presupposes an ordering. We apply these completeness results in order to obtain complete axiomatizations of the complex numbers.