I think that calling numbers with a sqrt(-1) component "imaginary numbers" was a terrible decision. It makes a lot of people, especially students, think of them as pure-math nonsense without any practical applications. I think that "lateral numbers" would have been much better.
And irrational numbers and negative numbers should be called "extraordinary numbers" and "reflected numbers" of course, of course.
They are imaginary though. They aren't the only made up model/concept that has practical application, just take a look at positive charges or Newtonian physics