  Extended modular group $\bar{\Pi}=<R,T,U:R^2=T^2=U^3=(RT)^2=(RU)^2=1>$, where
$ R:z\rightarrow -\bar{z}, \sim
T:z\rightarrow\frac{-1}{z},\simU:z\rightarrow\frac{-1}{z +1} $, has been used
to study some properties of the binary quadratic forms whose base points lie in
the point set fundamental region $F_{\bar{\Pi}}$ (See \cite{Tekcan1, Flath}).
In this paper we look at how base points have been used in the study of
equivalent binary quadratic forms, and we prove that two positive definite
forms are equivalent if and only if the base point of one form is mapped onto
the base point of the other form under the action of the extended modular group
and any positive definite integral form can be transformed into the reduced
form of the same discriminant under the action of the extended modular group
and extend these results for the subset $\QQ^*(\sqrt{-n})$ of the imaginary
quadratic field $\QQ(\sqrt{-m})$.
