Comparative Study to Find the Square Roots of Complex Numbers

Abstract

Complex numbers have been a cornerstone in mathematics since their inception in the 16th century. Despite their wide-ranging applications in physics, engineering, and other sciences, solving quadratic equations and finding the square roots of complex numbers remain challenging. This study introduces a novel method for finding square roots of complex numbers and compares its effectiveness with De Moivre’s theorem. The research applies De Moivre’s theorem to solve complex equations and derives a new analytical method for simplifying these solutions. The study evaluates both methods by solving a series of quadratic equations and compares the results in terms of accuracy, efficiency, and computational simplicity. The new method provided solutions identical to those derived using De Moivre’s theorem but with a simplified computational process. It was observed that the proposed method reduces complexity, minimizes computational steps, and achieves faster results without sacrificing accuracy. The novel analytical method is a robust alternative to De Moivre’s theorem for solving complex quadratic equations and finding square roots. It demonstrates significant advantages in terms of simplicity and speed, making it a valuable tool for mathematical and practical applications. This approach offers a streamlined process for addressing complex problems, bridging theoretical and practical insights in mathematical problem-solving.