<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1794-1237</journal-id>
<journal-title><![CDATA[Revista EIA]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.EIA.Esc.Ing.Antioq]]></abbrev-journal-title>
<issn>1794-1237</issn>
<publisher>
<publisher-name><![CDATA[Escuela de ingenieria de Antioquia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1794-12372018000100097</article-id>
<article-id pub-id-type="doi">10.24050/reia.v15i29.1131</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[EL MÉTODO DE NEWTON PARA RAÍCES COMPLEJAS. FRACTALES EN EL PROBLEMA DE CAYLEY]]></article-title>
<article-title xml:lang="en"><![CDATA[NEWTON&#8217;S METHOD FOR COMPLEX ROOTS. FRACTALS IN CAYLEY&#8217;S PROBLEM]]></article-title>
<article-title xml:lang="pt"><![CDATA[O MÉTODO DO NEWTON PARA RAIZES COMPLEXAS. FRACTAIS NO PROBLEMA DO CAYLEY]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Terán-Tarapués]]></surname>
<given-names><![CDATA[Juneth Andrea]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rúa-Álvarez]]></surname>
<given-names><![CDATA[Catalina María]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Nariño  ]]></institution>
<addr-line><![CDATA[San Juan de Pasto Nariño]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Nariño Departamento de Matemáticas y Estadística ]]></institution>
<addr-line><![CDATA[San Juan de Pasto Nariño]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>15</volume>
<numero>29</numero>
<fpage>97</fpage>
<lpage>108</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1794-12372018000100097&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1794-12372018000100097&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1794-12372018000100097&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Cuando la búsqueda de la solución de un problema de aplicación implica la resolución de ecuaciones no lineales se hace uso de métodos numéricos. Siendo el método de Newton uno de los más usados debido a su versatilidad y agilidad, es de gran interés emplearlo especialmente para aproximar soluciones de sistemas de ecuaciones no lineales. Solucionar ecuaciones con variable compleja a través del método de Newton tiene una aplicación muy interesante en el campo de los fractales como es la del problema de Cayley y las figuras fractales que se producen a partir de la convergencia, divergencia e incluso la eficiencia del método. En este artículo se muestra el estudio del problema de Cayley a través de la generalización del método de Newton a 2. Además, se presentan algunos fractales producidos por iteraciones del método de Newton en los complejos.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT When the search for the solution of an application problem involves the resolution of nonlinear equations, numerical methods are used. Newton&#8217;s method is one of the most used because of its versatility and agility and due to this is an excellent option to approximate the solutions of non-linear equation systems. Solving equations with complex variable through Newton&#8217;s method has an interesting application in the field of fractals such as Cayley&#8217;s problem and the fractal figures produced by the convergence, divergence and efficiency of the method. In this paper the study of the Cayley&#8217;s problem is presented through the generalization of Newton&#8217;s method to 2. In addition, are presented some fractal produced by iterations of the Newton&#8217;s method in the complex plane.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[RESUMO A procura da solução de um problema de aplicação envolve a resolução de equações não-lineares as vezes consegue-se com o uso de métodos numéricos. O método de Newton é muito utilizado devido à sua versatilidade e agilidade, sendo de grande interesse usá-lo para aproximar soluções de sistemas de equações não-lineares. Resolver equações com variáveis complexas através do método Newton tem uma aplicação interessante no campo dos fractais como é o problema de Cayley e as figuras fractais produzidas a partir da convergência, divergência e até mesmo a eficiência. Este artigo descreve o estudo do problema de Cayley desde a generalização do método de Newton a 2. Além disso, apresenta-se alguns fractais produzidos por iterações do método de Newton no plano complexo.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Método de Newton]]></kwd>
<kwd lng="es"><![CDATA[Sistemas de ecuaciones]]></kwd>
<kwd lng="es"><![CDATA[Raíces complejas]]></kwd>
<kwd lng="es"><![CDATA[Problema de Cayley]]></kwd>
<kwd lng="es"><![CDATA[Fractal]]></kwd>
<kwd lng="en"><![CDATA[Newton&#8217;s method]]></kwd>
<kwd lng="en"><![CDATA[Non-linear equation system]]></kwd>
<kwd lng="en"><![CDATA[Complex roots]]></kwd>
<kwd lng="en"><![CDATA[Cayley&#8217;s problem]]></kwd>
<kwd lng="en"><![CDATA[Fractal]]></kwd>
<kwd lng="pt"><![CDATA[Método de Newton]]></kwd>
<kwd lng="pt"><![CDATA[Sistemas de equações]]></kwd>
<kwd lng="pt"><![CDATA[Raízes complexas]]></kwd>
<kwd lng="pt"><![CDATA[Problema de Cayley]]></kwd>
<kwd lng="pt"><![CDATA[Fractal]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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