As we all know, a justification of the need for imaginary numbers is so that every polynomial of degree n has exactly n roots. And so the set of all numbers must contain more than just the reals.

By the same argument, the set of all words is incomplete owing to the existence of unanswerable questions.
Adding new words, imaginary words, may help answer these questions. Also by the same argument, any unresolved conflict in the world is evidence that there is more world out there; I propose to call this iWorld, or Worldi. We set sail tomorrow, who's with me?

I love it. I think I live there. I'm always dreaming about new ways to get around internal conflicts. And some of those ways involve ideas that I could find no words for.

What I could never figure out about imaginary numbers was DeMoivre's theorem. How repetitive functions like sines and cosines could come out of e^(ix) is beyond me.

Nice! I've always thought that those imaginary numbers do in fact exist, and the fact that we use the pejorative 'imaginary' only indicates the wimpy scope of the human imagination. Similarly, if the Many Worlds quantum theory is rea- is correct, then...well, skip it. iWorld sounds Macintoshy, but I'd like to board the ship if I'm welcome. This statement is non-self-referencing, and it's also false!

Good as far as it goes, but would this not be better represented by reference to the Cube Roots of Unity ? One "real" root and two opposed "imaginary" ones. These are the ones that give rise to the "conflict".

As an engineer, I must also put in a bid for "jWorld". Morning pastry to you, Lubbit.

What question would the imaginary word be the answer to? (Since the imaginary numbers are all built around asking what is the square root of minus one, could all imaginary words be constructed from one basic word?)

In my field, the imaginary quantity comes from the sinusoidal response being out of phase with the input, measured in milliradians. I'll therefore put up the name phiWorld for your perusal, and suggest that anyone who's slightly out of phase/step with conventional reality belongs here. One phiCroissant for you, lubbit.

[pottedstu] I nominate the sound "ummmm" (it would have to be spelt with non-existent letters though) as the imaginary word upon which all others are built.

Isn't this what fiction is partialy about? Lots fiction especialy Sci-Fi creates worlds difrent from our own to experiment with ideas. With imaginary numbers each question leads to a difrent [but related number], so each question we seek to answer with [i|j|phi]Worlds should lead to a difrent imaginary world.
For example if we want to know weather language affects the way we understand our enviroment we can create an imaginary world with whatever starting criteria we like.
Eventually we should find a power set of worlds, that give rise to all possible worlds, and then who knows what could happen...