Complex number and its conjugate in continued fraction

Abstract

For any equation complex roots occur in pairs. For finding a root of the equation in continued fractions algorithms are available. But to get complex roots in continued fraction no such procedure so far we have. Here, in this paper if α + iβ has a representation in continued fractions we try to find its conjugate α- iβ in terms of continued fractions. This will be useful in finding complex roots of a quadratic equations in continued fraction.