Example 1
Let
![$f(w)=u\cdot w$](img274.gif)
, where
![$u$](img275.gif)
and
![$w$](img56.gif)
are in
![$\mathbb {C}_{2}$](img48.gif)
. If
![$u\not\equiv 0$](img276.gif)
is noninvertible then, f is not quasiregular. If
![$u$](img275.gif)
is
invertible, then
![$f$](img9.gif)
is
![$K$](img27.gif)
-quasiregular for
where
![$u=u_1+u_2i_2.$](img278.gif)
In particular, if
![$u\in\mathbb {C}_{1}$](img279.gif)
, then
![$f$](img9.gif)
is conformal. However, we note in this example, that
![$f:\mathbb {C}^{2}
\longrightarrow\mathbb {C}^{2}$](img24.gif)
is a linear transformation which is nondegenerate if and only if
![$u$](img275.gif)
is invertible.