'complexly-administered' originates from the combination of 'complexly' and 'administered'. 'Complexly' comes from 'complex', which originates from Latin 'complexus', meaning 'embraced' or 'entwined'. 'Administered' comes from Latin 'administrare', meaning 'to manage'.

'complexly-administered' evolved from the combination of 'complexly' and 'administered', which were used separately in Middle English and later combined in modern English.

Initially, 'complexly-administered' meant 'managed in a complex manner', and this meaning has largely remained the same in modern usage.