Tarea 2 Numeros Complejos

\documentclass[a4paper]{article}

\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage[colorinlistoftodos]{todonotes}

\title{Tarea 2 Numeros Complejos}

\author{GALLARDO ZATARAIN CECILIA MICHELL  14210440}

\date{25 Agosto, 2014}

\begin{document}
\maketitle


\LARGE Resuelve lo siguiente



Z = 1 + 2i		

W = 5 + 3i		

V = 4 + i		




1)X.W

2)$\bar{W} -  \bar{V}$

3)6W+2Z



\section{Ejercicio 1}
1)X.W =

$(1+2i)(5+3i) = 5+31+10+6^2 = 5+13i-6 = -1+13i$

$z =-1+13i$

$ \bar {z} = -1-13i$

$\left | z \right | = \sqrt{  \alpha^2 + \beta^2} = \sqrt{ (-1)^2 + (-13)^2} = \sqrt{170}$
\begin{figure}
\centering
\includegraphics[width=0.3\textwidth]{graf_1}

\end{figure}

$\theta = \Pi- (tan^-1(\frac {13} {-1})) = 1.6475 $







\section{Ejercicio 2}

2)$\bar{w} - \bar{v}$ =

$(5-3i)-(4-i) = 5-3i-4+i = 1-2i$

$z =-1-2i$

$ \bar {z} = -1+2i$

$\left | z \right | = \sqrt{  \alpha^2 + \beta^2} = \sqrt{ (1)^2 + (-2)^2} = \sqrt{5}$
\begin{figure}
\centering
\includegraphics[width=0.3\textwidth]{GRAF2}
\end{figure}

$\theta = 2\Pi- (tan^-1(\frac {-2} {1})) = 5.1760 $




\section{Ejercicio 3}

3)6w+2z =

$6(5+3i)-2(1+2i) = 30+18i+2+4i = 32+22i$

$z =32+22i$

$ \bar {z} = 32+22i$

$\left | z \right | = \sqrt{  \alpha^2 + \beta^2} = \sqrt{ (32)^2 + (22)^2} = \sqrt{1024+484} = \sqrt{1580}$

$\theta = (tan^-1(\frac {22} {32})) = 0.6022 $

\begin{figure}
\centering
\includegraphics[width=0.3\textwidth]{GRAF3}

\end{figure}



\end{document}