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[SPAM] [obm-l] Re: [obm-l] Equação em Complexo

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Subject: [SPAM] [obm-l] Re: [obm-l] Equação em Complexo
From: "Gustavo Duarte" <gvduarte@xxxxxxxxxxxxxx>
Date: Sun, 9 Mar 2008 13:34:56 -0300
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Valeu Salhab, muit=EDssimo obrigado, ent=E3o o primeiro caso x^4 - 36 =
pude fazer por bi-quadrada, chamando x^2 de um K qualquer, achando K =
encontrei os 4 valores de x, por=E9m esse que eu tive d=FAvidas, x^4 + =
36,n=E3o seria uma boa op=E7=E3o (bi-quadrada) fazer a mudan=E7a de =
vari=E1vel  passando para uma equa=E7=E3o do 2 =BA grau e sim =
aplica=E7=E3o  direta da segunda f=F3rmula de  DE MOIVRE( =
radicia=E7=E3o),que eu n=E3o tinha notado !!captei corretamente sua =
mensagem ? acho que sim e mais um vz sou grato por socializar o =
conhecimento. obg.
  ----- Original Message -----=20
  From: Marcelo Salhab Brogliato=20
  To: obm-l@xxxxxxxxxxxxxx=20
  Sent: Sunday, March 09, 2008 11:05 AM
  Subject: Re: [obm-l] Equa=E7=E3o em Complexo


  Ol=E1 Gustavo,

  =E9 quase a mesma coisa:
  x^4 =3D -36 =3D 36 cis(180 + 360k)

  assim, x =3D rz(6) cis(45 + 90k)
  que sao: x =3D rz(6) cis(45), rz(6) cis(135), rz(6) cis(225), rz(6) =
cis(315)

  agora, basta passar pra forma retangular.. por exemplo:
  x =3D rz(6) cis(45) =3D rz(6) [ rz(2)/2 + i rz(2)/2 ] =3D rz(3) + i =
rz(3)

  abra=E7os,
  Salhab



  On Sun, Mar 9, 2008 at 10:28 AM, Gustavo Duarte =
<gvduarte@xxxxxxxxxxxxxx> wrote:

    x^4 - 36 =3D 0, tudo bem,encontrei como raizes : + rz(6), =
-rz(6),+rz(6)i e -rz(6)i   com  rz(X) >> raiz quadrada de x, por=E9m =
fiquei pensando no seguinte caso  :x^4 + 36 =3D0, desde j=E1 agrade=E7o =
alguma ajuda !!!



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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.6000.16608" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Valeu Salhab, muit=EDssimo obrigado, =
ent=E3o o primeiro=20
caso x^4 - 36 pude fazer por bi-quadrada, chamando x^2 de um K qualquer, =
achando=20
K encontrei os 4 valores de x, por=E9m esse que eu tive d=FAvidas, =
<STRONG>x^4 +=20
36,</STRONG>n=E3o seria uma boa op=E7=E3o (bi-quadrada) fazer a =
mudan=E7a de=20
vari=E1vel&nbsp; passando para uma equa=E7=E3o do 2 =BA grau e sim =
aplica=E7=E3o&nbsp;=20
direta da segunda f=F3rmula de&nbsp; DE MOIVRE( radicia=E7=E3o),que eu =
n=E3o tinha=20
notado&nbsp;!!captei corretamente sua mensagem ? acho que sim e mais =
um&nbsp;vz=20
sou grato por socializar o conhecimento.&nbsp;obg.</FONT></DIV>
<BLOCKQUOTE=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
  <DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
  <DIV=20
  style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
  <A title=3Dmsbrogli@xxxxxxxxx =
href=3D"mailto:msbrogli@xxxxxxxxx";>Marcelo Salhab=20
  Brogliato</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=3Dobm-l@xxxxxxxxxxxxxx=20
  href=3D"mailto:obm-l@xxxxxxxxxxxxxx";>obm-l@xxxxxxxxxxxxxx</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Sunday, March 09, 2008 =
11:05=20
  AM</DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Subject:</B> Re: [obm-l] =
Equa=E7=E3o em=20
  Complexo</DIV>
  <DIV><BR></DIV>Ol=E1 Gustavo,<BR><BR>=E9 quase a mesma coisa:<BR>x^4 =
=3D -36 =3D 36=20
  cis(180 + 360k)<BR><BR>assim, x =3D rz(6) cis(45 + 90k)<BR>que sao: x =
=3D rz(6)=20
  cis(45), rz(6) cis(135), rz(6) cis(225), rz(6) cis(315)<BR><BR>agora, =
basta=20
  passar pra forma retangular.. por exemplo:<BR>x =3D rz(6) cis(45) =3D =
rz(6) [=20
  rz(2)/2 + i rz(2)/2 ] =3D rz(3) + i =
rz(3)<BR><BR>abra=E7os,<BR>Salhab<BR><BR><BR>
  <DIV class=3Dgmail_quote>On Sun, Mar 9, 2008 at 10:28 AM, Gustavo =
Duarte &lt;<A=20
  =
href=3D"mailto:gvduarte@xxxxxxxxxxxxxx";>gvduarte@xxxxxxxxxxxxxx</A>&gt;=20
  wrote:<BR>
  <BLOCKQUOTE class=3Dgmail_quote=20
  style=3D"PADDING-LEFT: 1ex; MARGIN: 0pt 0pt 0pt 0.8ex; BORDER-LEFT: =
rgb(204,204,204) 1px solid">
    <DIV bgcolor=3D"#ffffff">
    <DIV><FONT face=3DArial size=3D2><B>x^4 - 36 =3D 0,</B> tudo =
bem,encontrei como=20
    raizes :&nbsp;+&nbsp;rz(6), -rz(6),+rz(6)i e=20
    -rz(6)i&nbsp;&nbsp;&nbsp;com&nbsp; <I>rz(X) &gt;&gt; raiz quadrada =
de=20
    x,</I><B> </B>por=E9m fiquei pensando no seguinte caso&nbsp; :<FONT=20
    size=3D3><B>x^4 <FONT color=3D#ff0000>+ </FONT>36 =3D0, </B>desde =
j=E1 agrade=E7o=20
    alguma ajuda !!!</FONT></FONT></DIV>
    <DIV><B><FONT face=3DArial=20
  =
size=3D2></FONT></B>&nbsp;</DIV></DIV></BLOCKQUOTE></DIV><BR></BLOCKQUOTE=
></BODY></HTML>

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References:
- [SPAM] [obm-l] Equação em Complexo
  - From: Gustavo Duarte
- Re: [obm-l] Equação em Complexo
  - From: Marcelo Salhab Brogliato

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