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MathGroup Archive 2001

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Re: Factor[1+x^4]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26866] Re: [mg26855] Factor[1+x^4]
  • From: Matt.Johnson at autolivasp.com
  • Date: Fri, 26 Jan 2001 01:27:16 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Tom:

This will produce the factors:
In[14]:=
factors = Solve[1 + x^4 == 0, x]
Out[14]=
\!\({{x -> \(-\((\(-1\))\)\^\(1/4\)\)}, {x -> \((\(-1\))\)\^\(1/4\)}, {x -> \
\(-\((\(-1\))\)\^\(3/4\)\)}, {x -> \((\(-1\))\)\^\(3/4\)}}\)

This will put them in complex form:
In[15]:=
ComplexExpand[x /. factors]
Out[15]=
\!\({\(-\(\(1 + \[ImaginaryI]\)\/\@2\)\), \(1 + \[ImaginaryI]\)\/\@2, \(1 - \
\[ImaginaryI]\)\/\@2, \(-\(\(1 - \[ImaginaryI]\)\/\@2\)\)}\)

-matt





"Tom Cage" <k5gj at earthlink.net> on 01/24/2001 11:13:31 PM

cc:
Subject: [mg26866]  [mg26855] Factor[1+x^4]



I would like to factor 1+x^4.   Mathematica 3 will only respond with
In[1]:= Factor[1+x^4]
Out[2]= 1+x^4


    Other systems will give the complex result

1+x^4 = (x+1/2*Sqrt(2)*I+1/2*Sqrt(2))*
        (x+1/2*Sqrt(2)*I-1/2*Sqrt(2))*
        (x-1/2*Sqrt(2)*I+1/2*Sqrt(2))*
        (x-1/2*Sqrt(2)*I-1/2*Sqrt(2))


    How would I factor 1+x^4 with Mathematica









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