 Since a simple equivalence transformation shows that

whenever "z" ≠ 0, the preceding result for the continued fraction "y" can be restated for "x".The infinite periodic continued fraction

converges if and only if "z"2 is not a real number lying in the interval −4 < "z"2 ≤ 0 – or, equivalently, "x" converges if and only if "z" ≠ 0 and "z" is not a pure imaginary number with imaginary part between -2 and 2.