Etymology
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imaginary (adj.)

"not real, existing only in fancy," late 14c., ymaginaire, from imagine + -ary; or else from Late Latin imaginarius "seeming, fancied," also literal, "pertaining to an image," from Latin imaginari "picture to oneself." Imaginary friend (one who does not exist) attested by 1789.

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Definitions of imaginary
1
imaginary (n.)
(mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1;
Synonyms: complex number / complex quantity / imaginary number
2
imaginary (adj.)
not based on fact; existing only in the imagination; "the falsehood about some fanciful secret treaties"- F.D.Roosevelt;
a small child's imaginary friends
Synonyms: fanciful / notional
From wordnet.princeton.edu