Hi, everybody.

I am second-guessing myself with this question: Can Newton’s Method (a.k.a. the Newton-Raphson Method) be used to compute complex roots? I had assumed that it could not; it always seems to be mentioned in the context of computing real roots and all the examples I have seen used to illustrate the method use equations with real roots. However, I don’t think I have ever seen it explicitly stated anywhere that Newton’s Method can not be used to find complex roots. In addition, somebody working on a solver for a cubic polynomial indicated that it could be. So now I am wondering.


Can Newton’s Method be used to compute complex roots?

In case anybody else is wondering about this, Newton's Method can be used to solve for complex roots. The important thing to keep in mind for these cases is to use a complex point as the initial point, otherwise the algorithm doesn't leave the real axis.

(Incidentally, the secant method can be used to solve for complex roots too.)