Design and use of a learning object for finding complex polynomial roots

Abstract

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we present several applications of this learning object: study of several transformations in the plane, the problems appearing in numerical analysis concerning roots of complex polynomials with the same modulus or whose multiplicity is greater than 1, the continuity of the roots depending on the coefficients of the polynomial and the study of a classical curve. Interactive learning objects can improve the students' ability, if in addition, they are under suitable guidance.

Keywords:

• polynomial equations
• complex-valued functions
• fundamental theorem of algebra
• learning objects