ATOM Volume XIII: Quadratics and Complex Numbers

While the quadratic equation is part of the standard syllabus in secondary school, the scope of this topic has been curtailed in many jurisdictions over the years. It is not enough for students to simply do basic factoring exercises and engage in rote application of the quadratic formula in solving equations. This criticism has even more force when it comes to the topic of complex numbers. For many students, complex numbers arise only in the discussion of the roots of a quadratic equation with negative discriminant. Students have no idea of their theoretical and utilitarian importance in mathematics. This book is intended as a companion to the usual high school fare. The reader is assumed to have been introduced to polynomials and operations of addition, subtraction, multiplication and division, the remainder and factor theorems, simple factorizations, solution of quadratic equations by factoring, completing the square and the quadratic formula, and the relationship between the roots and coefficients of a quadratic equation. In addition, the reader should know the fundamental trigonometric functions and their values at standard angles as well as simple relationships among them.