Aspecto histórico e desenvolvimento de números complexos: aplicação das fórmulas de Moivre na área da geometria plana
The present article has as its theme History of complex numbers and calculation of roots from the rotation of a regular polygon inscribed in the circumference and seeks to make a brief historical approach to the emergence of complex numbers in the renaissance period that resulted in the development...
| Autor principal: | OLIVEIRA, Jefferson Nahum de |
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| Grau: | Trabalho de Conclusão de Curso - Graduação |
| Idioma: | por |
| Publicado em: |
2022
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| Acesso em linha: |
https://bdm.ufpa.br:8443/jspui/handle/prefix/3926 |
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The present article has as its theme History of complex numbers and calculation of roots from the rotation of a regular polygon inscribed in the circumference and seeks to make a brief historical approach to the emergence of complex numbers in the renaissance period that resulted in the development of the complex set and of algebraic properties of quadratic and cubic equations. Another approach focuses on the Argand-Gauss plane and de Moivre formulas with applications to regular polygons inscribed in the circle of unit radius. Inserted in this context, it dedicates and emphasizes an analytical process related to regular polygon rotations in a unit radius circle to obtain coordinates of a polygon with n sides without the need to use the 2nd Moivre formula. This teaching process is applied to regular polygons of n sides, showing how to find all the roots of each of their vertices. The research concludes considering that the analytical procedure used without the need to involve the 2nd formula of Moivre, represents an interesting teaching strategy to calculate nth roots of a complex number. |