CHAPTER 8 - COMPLEX NUMBERS AND THE FUNDAMENTAL THEOREM OF ALGEBRA

Abstract

This chapter discusses the fundamental theorem of algebra, which states every polynomial P(x) of degree n > 1 has at least one root among the complex numbers. The root guaranteed by this theorem may be a real number as the real numbers are a subset of the complex number system. The chapter also presents alternative form of the fundamental theorem of algebra, which states that if P(x) is a polynomial of degree n > 1, then P(x) has precisely n roots among the complex numbers when a root of multiplicity k is counted k times. The conjugate theorem extends the result that if a quadratic equation with real coefficients has a complex root a + bi, then the conjugate a − bi is the other root, to a polynomial of degree n with real coefficients. The chapter discusses the polynomials with real coefficients.