Solving Quadratic Equations with Complex Coefficients & Determining the Square Root for any Complex Number
Aziz Arbai *
ENSIT - Ecole des Nouvelles Sciences d’ingenierie - Le Laboratoire Systemes, Controle et Decision (LSCD), Tanger, Morocco.
Amina Bellekbir
Faculty of Sciences, Abdelmalek Essaadi University, Tetouan, Morocco.
Abounaima Mohammed Chaouki
Faculty of Sciences and Technology, Sidi Mohammed Ben Abdellah University, Fes, Morocco.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a definitive solution for expressing the second root (z1/2) of any complex number z as a function of z and Δ1/2 as a function of Δ in the context of quadratic equations with complex coefficients. This research has resulted in two direct algorithms and associated software. These algorithms are not only accurate but also exceptionally fast, providing a powerful tool for efficiently determining the second root of any complex number and solving quadratic equations with complex coefficients. This innovative approach addresses a long-standing challenge in the field, significantly contributing to the accuracy and speed of calculations in complex coefficient scenarios either manually or using a programmable computing machine such as smart phones or computers.
Keywords: Complex numbers, equations of the second degree, algorithm, the second root