  We describe various properties of continued fraction expansions of complex
numbers in terms of Gaussian integers. Numerous distinct such expansions are
possible for a complex number. They can be arrived at through various
algorithms, as also in a more general way from what we call "iteration
sequences". We consider in this broader context the analogues of the Lagrange
theorem characterizing quadratic surds, the growth properties of the
denominators of the convergents, and the overall relation between sequences
satisfying certain conditions, in terms of nonoccurrence of certain finite
blocks, and the sequences involved in continued fraction expansions. The
results are also applied to describe a class of binary quadratic forms with
complex coefficients whose values over the set of pairs of Gaussian integers
form a dense set of complex numbers.
