Solving Quadratic Equations with Complex Coefficients & Determining the Square Root for any Complex Number

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.