  We study the generalized continued fraction expansions of complex numbers in
term of elements from Euclidean subrings, especially Gaussian or Eisenstein
integers, in a general framework as pursued in [3] and [1]. We introduce a
common approach to studying the continued fraction expansions of zeroes of
binary forms, via consideration of the action of the general linear group, and
apply it to discuss expansions of quadratic surds on the one hand and of badly
approximable numbers on the other hand. Also, we generalize the property of the
simple continued fraction expansions that the convergents are the "best
approximants", to a large class of continued fraction expansions of complex
numbers.
