The term "Complex" comes from the USA. The JAA have to some extent copied the FARs in producing JARs they do not however mention the word "Complex" they merely state that familiarisation training is required if you fly an aeroplane with any of the following features:
Tail wheel
VP Prop
Retractable U/C
Turbo/Supercharger
Presuruisation
So those who use the term "Complex" are like those who call all ball pens "Biros"