imaginary adj.

mid-14c., "to form a mental image of," from Old French imaginer "sculpt, carve, paint; decorate, embellish" (13c.), from Latin imaginari "to form a mental picture, picture to oneself, imagine" (also, in Late Latin imaginare "to form an image of, represent"), from imago "an image, a likeness," from stem of imitari "to copy, imitate" (from PIE root *aim- "to copy"). Sense of "suppose, assume" is first recorded late 14c. Related: Imagined; imagining.

adjective and noun word-forming element, in most cases from Latin -arius, -aria, -arium "connected with, pertaining to; the man engaged in," from PIE relational adjective suffix *-yo- "of or belonging to." The neuter of the adjectives in Latin also were often used as nouns (solarium "sundial," vivarium, honorarium, etc.). It appears in words borrowed from Latin in Middle English. In later borrowings from Latin to French, it became -aire and passed into Middle English as -arie, subsequently -ary.

Proto-Indo-European root meaning "to copy." 

It forms all or part of: emulate; emulation; emulous;  image; imaginary; imagination; imaginative; imagine; imago; imitable; imitate; imitative; imitator; inimitable.

It is the hypothetical source of/evidence for its existence is provided by: Latin imago "image," aemulus "emulous," imitari "to copy, portray, imitate;" Hittite himma- "imitation, substitute."