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From: Webster's Revised Unabridged Dictionary (1913)

 Im·ag·i·na·ry a.  Existing only in imagination or fancy; not real; fancied; visionary; ideal.
 Wilt thou add to all the griefs I suffer
 Imaginary ills and fancied tortures?   --Addison.
 Imaginary calculus See under Calculus.
 Imaginary expression  or Imaginary quantity Alg., an algebraic expression which involves the impossible operation of taking the square root of a negative quantity; as, √-9, a + b √-1.
 Imaginary points, lines, surfaces, etc. Geom., points, lines, surfaces, etc., imagined to exist, although by reason of certain changes of a figure they have in fact ceased to have a real existence.
 Syn: -- Ideal; fanciful; chimerical; visionary; fancied; unreal; illusive.