A complex continued fraction is a continued fraction whose partial quotients are complex numbers. It commonly has the form
 |
where the 
are often Gaussian integers. Its convergents
are obtained from the same recurrence relations
as those of an ordinary continued fraction.
Unlike the real numbers, the complex numbers have no natural ordering with which to select an integer part. A complex continued fraction algorithm must therefore specify a fundamental region or another rule for choosing the partial quotients. The nearest Gaussian integer algorithm and the Schmidt algorithm are examples.
