Banca de DEFESA: RAFAEL DANTAS SOBRINHO

The Rule of Dual Terms: An Interpretation of Cramer's Method at the Complex Plane

APPLICATIONS. COMPLEX NUMBERS. LINEAR SYSTEMS.

In High School, there is a lack of interesting applications related to the study of complex num-bers, which is sometimes reflected in an arid approach to this topic, which is, almost, yourcharacteristic. In this work, we aim to provide for the teacher unusual applications of alge-bra and geometry of complexes, through which he can motivate and illustrate his classes byteaching them, connecting them to the resolution and discussion of linear systems with smalldimension overR. In this context, we will establish an interpretation of Cramer’s method in thecomplex plane, which we will call the “Rule of Dual Terms”. This will require, by extension,the acts of defining and exploring the “Horizontal and Vertical Transliners of SpaceMn×m(C)”which we will prove to be diagonalizable automorphisms.