But it must change the language

I think the naming is historically due to Cardano's trick of assuming existence of « imaginary » solutions of the auxiliary 2nd degree equations that are used for solving 3rd degree equations in the case where the discriminant is negative, in a trick that must have looked incredibly artificial at the time. *That* was thinking out of the box !

The geometric interpretations came much later, and while useful in countless cases, it's just one way to think about complex numbers, that's not adapted to all settings.

Anyway, getting back on topic, sorry.