Bezout's equation for Gaussian integers and Z[√2]

The Euclidean algorithm for Gaussian integers, properly done, starts with Gaussian integers a and b and calculates Gaussian integers s and t such that sa + tb divides both a and b. It follows that sa + tb is a greatest common divisor of a and b.

This program accepts Gaussian integers in the form 3 + 2i, or elements of Z[√2] in the form 3 + 2r, where r stands for √2 (but not simultaneously).
a =   b =