Imaginary numbers are defined. Imaginary numbers are not rotations or anything else that I keep hearing. Those are all properties of the fact that we define an imaginary number to be z = a + bi, where a and b are real numbers, and i^2 = -1. That's it.
If someone asks what is an imaginary number the correct answer is "z = a+bi, where a and b are real numbers, and i^2 = -1".