euclidean algorithm for complex numbers

>>7782907
reducing to reach what form?

>>7782915
[math]a\,=\,b\,q\,+\,r[/math] where [math]q[/math] is the greatest complex number smaller than [math]\lfloor \frac{a}{b} \rfloor[/math] and [math]0\,\leqslant r \,\leqslant b\,-\,1[/math].

>>7782925
ok, what definition of inequalities in C do you choose?

For complex numbers in general, you can just divide a/b. I'm assuming you're referring to complex numbers where the real and imaginary parts are integers, those are called Gaussian Integers and you can indeed use a kind of euclidean algorithm. Any system with this property is called an Euclidean domain, see this link for an example using the Gaussian Integers
http://mathforum.org/library/drmath/view/67068.html