You mean limit of sqrt(x) when x->+inf = +inf

You’re missing the point. Math (especially advanced) is about precision and rigor. Writing sqrt of something negative is ambiguous. There are better ways of writing it as explained here https://lemmy.world/comment/18924227

Square root definition does not allow a negative number as an input. Only positives and zero. Although it is possible to expand the definition to negative numbers, complex numbers, matrices… So unless you followed a course where you thoroughly defined your expansion of sqrt, it only applies to real, positives number and zero. Its the thing with math, you have to define what you work with.

In my case, I did prep courses for entrance exam to engineering schools (something like in dead poet society but more modern), using sqrt(-1) somewhere would be an instant 0 mark. Like forgetting a unit in a physics test answer.

Sqrt(-1) is still wrong tho. I’m commuting a sin by writting it. Correct expression is i^2=-1