First I have a simple question for you: Are you incapable of using proper English constructions? Why do you make yourself look foolish by using "chat-speak" when discussing a serious topic.

Second, there is no such thing as "

underroot(-1)" If you are serious then learn to use symbols. [TEX]\sqrt{-1}[/TEX] gives $\displaystyle \sqrt{-1}$. You are not too lazy to take the time to type that are you?

Now to your question. If I were living pre-sixteenth century and saw "$\displaystyle \sqrt{-1}$", I would say "what fool wrote that?'

But from the year 1609 on, the idea of complex numbers has become well understood. It has been developed into a consistent theory.

Do you even understand that "iota", $\displaystyle \iota$ is a Greek letter not to be confused with the mathematical symbol $\displaystyle i$, which is used to stand for the principal root of $\displaystyle x^2+1=0~?$

And that is you answer as to what is is used for: it completes the number system giving us the

fundamental theorem of algebra.