I almost posed this as a proper "Problem," but just couldn't bring myself to actually do so. I like it better as a jumping-off point for a discussion.
What is the area of a triangle whose sides have lengths \(3+i\), \(3+2i\) and \(4-3i\)?
Yes, it's a little ridiculous, but that's intentional. After all, we mathematicians, like the White Queen in Through the Looking-Glass, sometimes like to believe "six impossible things before breakfast."
Is it possible to make any sense out of such a question? Is there an answer? What does it mean?
What other questions do you find yourself asking?