Definitions for complex numbers

I recently said that it seemed very surprising to me that we could find complex roots (like x'=-2+9i or x"=5-2i).
In my school, this doesn't exist.
It seems to be an abstract and useless mathematical construct, which only serves to confuse the minds of young students for very little purpose—in short, a huge waste of time and energy.
I'm not talking about Gauss-Argand coordinate systems, which are "something else." I'm talking about the roots of all Cartesian functions on a plane xOy.
It's very easy for those who read me to believe me when I tell them that the real roots of an equation like x²-5x+4 are PURE REALS.
And they set x'=1 and x"=4, probably thinking that I'm the greatest mathematician in the world and that I should award the Fields Medal.
But they dispute this medal if I tell them that, similarly, when there are imaginary roots, we shouldn't talk about complex roots, but about pure imaginary roots, and that the notations specified above are as ridiculous as they are useless.
This time, let's take f(x)=x²+4. Both roots are imaginary, not "complex," a much-misused term. Here, as should always be the case, we have an answer written in pure imaginary.
x'=2i and x=-2i. Points that we place as A(-2,0) and B(2,0) from left to right. Since the iOi' axis is drawn from right to left.
Thank you for listening.
R.H.