What does "imaginary" mean?

Imaginary: 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 quantity (Alg.), an algebraic expression which involves the impossible operation of taking the square root of a negative quantity; as, sq. root-9, a + b sq. root-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.