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Les Evans, "Complex numbers and vectors (Series: MathsWorks for teachers)"

COMPLEX NUMBERS AND VECTORS IN THE SECONDARY CURRICULUM INTRODUCTION Complex numbers and vectors are both important areas of study within the senior secondary mathematics curriculum. The rationale for the inclusion of complex numbers in the curriculum is often related to: arguments for completeness of algebraic analysis of polynomial functions and the solution of related equations consideration of certain types of transformations of the (complex) plane, in particular those involving combinations of dilations and rotations, as well as some curves and regions in the complex plane Students typically encounter complex numbers in the guise of some kind of special number that enables one to extend certain algebraic manipulations on quadratic functions of a real variable with real coefficients to ensure that the rule of any quadratic function q]g x = ax + bx + c can be expressed as a product of two linear factors, and the equations q]g x = 0 always has two (not necessarily distinct) roots. The best problems can appear deceptively simple, but can create the need to explore new ways of thinking about our world and how we choose to describe it. A small problem may allow an insight. Student Activity 2.1 can be used to illustrate this point to students.

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