A New Technique to Compute Complex Roots

Abstract

In this paper we modified Newton-Raphson and Secant methods to Complex form, then from that we get new iterative formula to them, named Newton (Secant) real iteration formula and Newton (Secant) imaginary iteration formula, real iteration used to find real roots while imaginary iteration one will be used to find complex roots of non-linear equations such as (0 2   a x). To find real roots, we start with a real initial point in real iteration getting a sequence of real numbers, to find complex roots start with a complex initial point in complex formula getting a sequence of complex numbers, also we write a new algorithm for this technique and write the program by using Matlab application system version 7.8 for this new method such that it will determine the real roots when we enter the initial real point but when we enter the initial complex point it will determine the complex roots.