Números complexos e a transformação de Mobius
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Data
2013-07-05
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Universidade Federal de Goiás
Resumo
The set of complex numbers arose from the necessity of expanding the
set of real numbers with the aim of solving algebraic equations. That has
happened in Europe in the sixteenth century. Great Italian mathematicians
as Scipione , Tartaglia, Cardano and Bombelli, contributed. This was the
initial step that now allows us to know the square root of a negative number.
A set numeric need not necessarily associated elements numbering, measuring
or a count. O set of parts, a set of objects, provided the operations
union and intersection, can be a set number even if its elements are not
numbers. The body unordered of the complex numbers is a set of numbers
(where the numbers are ordered pairs ) and can be represented by other
structures, isomorphs to this set as the square matrices as two or classes of
residual polynomial.
Certain complex functions contribute for a better understanding of geometric
transformations. The transformation of M obius is a good example
of complex function,applied on a curve that can generate the e ects of rotation,
translation, dilation (or contraction) and inversion.
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Pereira, Helder Rodrigues. Números complexos e a transformação de Mobius. 2013. 48 f. Dissertação (Mestrado em Matemática) - Programa de Pós-graduação em Matemática (IME) - Universidade Federal de Goiás - Goiânia, 2013.