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Weregoose
Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004
Posts: 3976
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 Posted: 01 Oct 2009 01:39:16 am Post subject: |
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I'm in a bit of a rut. Of the four solutions to [font="times new roman"]9 = | x – 7 e5 i |, the complex ones are very easy to find. The real-valued ones, however, I can't seem to magically pull out of thin air! How can I go from this expression to -4.009591764 and 7.980862361 without crawling on my hands and knees along the curve?
Last edited by Guest on 01 Oct 2009 01:43:49 am; edited 1 time in total |
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thornahawk
μολών λαβέ
Active Member
Joined: 27 Mar 2005
Posts: 569
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| Posted: 01 Oct 2009 07:07:55 am Post subject: |
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I don't know... isn't that equation the same as x² -14 cos(5)*x + 49 == 81 ?
How did I get to that quadratic, you ask? Remember that |z| == √ ((Re z)² + (Im z)²), treat x as a complex variable with zero imaginary part... you then have a quadratic with the roots you mentioned.
thornahawk |
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Weregoose
Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004
Posts: 3976
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| Posted: 01 Oct 2009 09:16:24 am Post subject: |
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Nuts! That's what I started with. :D
My motivation here is to reduce the number of symbols, but my techniques are pretty much exhausted. Is there really no other gap that we can squeeze into? Wait... Quadratic formula. Let me give this a shot.
1→Q
(A+θ)cos(θ→R
C[font="verdana"]²-A[font="verdana"]²→S
I can work with this! Thank you very much, sir. :)
[EDIT]
Hmm, blast it, this is no better. "R" appears twice and "S" appears twice, and they both have to be chosen from a list in a very special way... If I don't figure out a reasonably small way of doing this, then this section of code will be one very ugly duckling. 
Last edited by Guest on 05 Jul 2010 07:58:39 am; edited 1 time in total |
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thornahawk
μολών λαβέ
Active Member
Joined: 27 Mar 2005
Posts: 569
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| Posted: 01 Oct 2009 11:52:31 am Post subject: |
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As I thought, this isn't the full story. If you can't post publicly what exactly you're trying to accomplish, you can P.M. me what you have in mind; I may at least be able to point you to the literature if I can't think of something.
(Edit: Note BTW that the locus of [font="times new roman"]9 = | x – 7 e5 i | in the complex plane is a circle... so I'm a bit hazy on what you're saying are "four solutions" because there's a whole lot of them.)
thornahawk
Last edited by Guest on 02 Oct 2009 01:06:55 am; edited 1 time in total |
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