Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Having existence only in the imagination; unreal.
 adj. Mathematics Of or being the coefficient of the imaginary unit in a complex number.
 adj. Mathematics Of, involving, or being an imaginary number.
 adj. Mathematics Involving only a complex number of which the real part is zero.
 n. Mathematics An imaginary number.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. existing only in the imagination
 adj. of a number, having no real part; that part of a complex number which is a multiple of the square root of 1.
from the GNU version of the Collaborative International Dictionary of English
 adj. Existing only in imagination or fancy; not real; fancied; visionary; ideal.
 n. An imaginary expression or quantity.
from The Century Dictionary and Cyclopedia
 Existing only in imagination or fancy; due to erroneous belief or conception; not real; baseless; fancied: opposed to actual.
 In mathematics, unreal and feigned in accordance with the theory of imaginary quantities.
 Synonyms Ideal, fanciful, fancied, visionary, unreal, shadowy, Utopian. Imaginary and imaginative are never synonymous: imaginary means existing only in the imagination; imaginative means possessed of or showing an active imagination.
 n. In algebra, an imaginary expression or quantity.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. not based on fact; unreal
 n. (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of 1
Etymologies
Examples

Because Larry’s Fundy brain is so locked by his literalism he simply thinks “imaginary numbers” are *actually imaginary* ,that is to say not real, they do not exist.
The next time ID people cry 'censorship'  The Panda's Thumb

In fact, psychologists use the term "imaginary audience" to describe this heightened state of vigilance that is especially strong during adolescence.
Robert Pagliarini: Get Over Yourself! Learn This Secret to Boost Your Confidence

But on the other hand, as this warmth is felt differently by different temperaments, so what we call imaginary things affect different minds.

I write fantasy in imaginary worlds, but my settings are historically based.

It wasn't so much fun imagining loosing her senses, and she refers to the imaginary loss of her eyesight and hearing as "harrowing."

Their interests by virtue of public statements and the work made collectively between 1961 and 1966 appear largely designed to dissolve what in theater is known as the imaginary "fourth wall" dividing audiences from artists.
G. Roger Denson: You Say You Want a Revolution. Well You Know, Art Can Cure You of That

But her reference to "these signs"  as if placards charging individual troops with war crimes are commonplace at a "standard antiwar demonstration"  reveals that a powerful imaginary is at work.

Act in imaginary circumstances in order to learn more either about the self, or about a certain culture, or about others.

It should be a requirement that damages be documented, not in imaginary figures but in real life dollars as to the effect that the claimed damages are to be.

Vacuuming and dusting and mopping up the kitchen had helped calm Alvirah, and while she was working she had put on her “thinking cap,” as she called the imaginary head covering that helped her find solutions to problems.
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rolig commented on the word imaginary
Well, it can be done; it just takes some imagination.
The revery alone will do…
March 2, 2009
qroqqa commented on the word imaginary
And in fact the water would have to be a cuboidal volume sufficient to contain a hemisphere of Saturn, and that's got some gravity of its own (that's an emphatic 'some' . . . I wonder how you punctuate that?); not to mention the rigid material for the bath.
March 2, 2009
seanahan commented on the word imaginary
That's really not such a great analogy if you think about it too much. I'm pretty sure the gravitational pull of Saturn would do some things do a bathtub full of water. The whole idea of floating doesn't make a lot of sense on this scale.
March 2, 2009
qroqqa commented on the word imaginary
Saturn is the only planet in our solar system that is less dense than water. If you could build an imaginary gigantic bathtub, Saturn would float in it.
—National Geographic, trying to palm it off on NASA. No, if you built an imaginary bath, the water would still all fall through. You need to imagine building a real gigantic bath for this one.
February 23, 2009
thebighenry commented on the word imaginary
The autogenerated definition is mathematically correct for a complex number, though in common usage it also applies to an imaginary number. The mathematically correct definition for imaginary number is:
(n): (mathematics) a number of the form "bi" where "b" is a real number and i is the square root of 1
May 13, 2008
oroboros commented on the word imaginary
Imagine a comment.
November 5, 2007