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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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