You know, like that friend you had who was always causing trouble when you were... what? Numbers? Oh, you mean the ones that mathematicians spent centuries ignoring!
It's true! I mean, for a long time mathematicians didn't want to admit that zero or negative numbers were useful either, but that's another topic entirely. So, back in ancient Greece, this guy, Heron of Alexandria, taught at the Musaeum (you may heard of their library, it was kind of a big deal). This guy was cool. As in, he was researching cybernetics back around 50 AD and invented the first vending machine. And he quite possibly discovered imaginary numbers.
People didn't like those. The square root of a negative number? That didn't make any sense! Well, you know... until fluid dynamics, quantum mechanics, and vibration analysis. Girolamo Cardano said that working with them was "mental torture" and was "as subtle as it would be useless." Descartes first named them imaginary... as in, if you needed them to solve a problem, there wasn't actually a solution. It wasn't until the late 1700s (yes, that is 17 centuries after their discovery) that the mathematical community really began to recognize that these were real... okay, not "real", but also not fake, things.
So here's what I like best about imaginary numbers. Do you know what the complex plane looks like? Here, I'll show you...
So numbers on the y-axis are purely imaginary, and numbers on the x-axis are purely real. You know what means, right? It means you can change the message on your phone to say, "The number you have dialed is imaginary. Please rotate your phone ninety degrees and try again"! Wouldn't that be so awesome! ...Yeah, I'm probably the only one who thinks that it is, huh?
Oh, by the way, my friends were Binks, Boinks, and their dog named Max. Looking back, I'm fairly certain that Binks was an elf, Boinks was a construct, and Max was a mathematician, which explains so much... Did your imaginary friends like numbers too?