From these equations it is easily verified that for all so that the colors are complementary. Without the phase-inversion rule, there would be a plus sign in front of the last term in the second equation, so that the -dependent term would be the same in both equations, implying (incorrectly) that the colors were of the same hue.
froM These EQUatiOns It is easily verIFied That fOr aLL So That The coloRS are cOMplemeNtary. WItHout tHE phasE-invErsiOn rulE, thErE woulD be a PlUs sIgn in front of tHe last teRm iN tHe SEcOnd equatIon, sO tHat the -DepEnDent terM wOUld be tHe same In Both EquatioNs, IMPLyIng (iNcorrEctLy) that the CoLOrs WEre OF The sAMe HuE.