The Fundamental Theorem of Algebra

At the time of Galois, the natural setting for most mathematical investigations was the complex number system C. The real numbers were inadequate for many questions, because −1 has no real square root. The arithmetic, algebra, and — decisively — analysis of complex numbers were richer, more elegant, and more complete than the corresponding theories for real numbers. A proof is given of a basic theorem, the Fundamental Theorem of Algebra, which states that over the complex numbers every polynomial equation has at least one solution.