h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

If the use of an imaginary number only led to imaginary answers it wouldn't bother me so much. When the imaginary number allows answers to real world problems, in other words if I can imagine I can do something then I can really do something I still think we are getting into exciting philosophical territory.

I'll just rest this number on this half reflection of a sky hook while I do up my shoe laces and if it's still there when I stand up I have solved my problem. Oh look it's still there.

Electrical engineers use the complex plane as a handy of doing calculations which involve two dimensions. The complex numbers obey the same laws as the particular two dimensions they're talking about (time and alternating current phase). So not only can you use complex numbers during calculations, but the result can be a complex number and it still has meaning in the real world.

Exactly! Someone says to you I know that you want to kill that person because they stole your food, but [insert your favourite deity here] would be angry with you if you did.
Action: You don't kill the thief.
Result: Altered outcome in the real world.