Imaginary is an adjective used to describe something or someone as being in one’s imagination, or not existing in reality. It is also commonly used in mathematics to a square root of a negative number, something which does not actually exist and can only be imaginary.
The adverb form of this word is imaginarily and the noun form is imaginariness.
Imaginative is also an adjective and can be used to describe something as not being real or pertaining to imagination. But it is not always a synonym of imaginary. It is used to describe something or someone as being creative or having a good imagination. Also, it is sometimes used to describe something as having to do with imagery or images.
The noun form is imaginativeness and the adverb form is imaginatively.
Sometimes, as in the second example below, the meaning of imaginative is unclear and could be interpreted as either not real or exceptionally creative. Be careful to keep meaning clear and use synonyms as appropriate.
My eyes are closed, my head is thrown back, and I’m pretending to conduct an imaginary orchestra to Beethoven’s ninth symphony, which is booming out of speakers above my head. [The Telegraph]
Wildly imaginative and deeply political, Miguel Gomes’s Arabian Nights portrays the struggles of working class Portuguese under extreme austerity measures.[Sydney Morning Herald]
The action scenes are “imaginative and suspenseful and gradually take on a demented exuberance,” LaSalle continues, and “although the film ultimately lacks that extra something that Spielberg often brings — the sense that the action is somehow emblematic of something grand in the human spirit — the movie has a caustic wit that will do in its place.” [LA Times]