PrimeLime
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#1
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I'm currently self-teaching FP2, using the online textbook provided by AQA (and managing to cope despite the plethora of mistakes in the book XD) and I've just reached the end of Chapter 4 which concerns de Moivre's theorem and its applications. But I am stuck on the last problem.

Could someone look at the last problem in Chapter 4 and give me some help? Preferably a small hint, NOT the whole solution. Here is the book: http://filestore.aqa.org.uk/subjects...2-TEXTBOOK.PDF
By the way it's the very last part I'm stuck on; I managed the rest of the question fine.

I want to know the most elegant/quickest method if possible. Thanks.
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kkboyk
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(Original post by PrimeLime)
I'm currently self-teaching FP2, using the online textbook provided by AQA (and managing to cope despite the plethora of mistakes in the book XD) and I've just reached the end of Chapter 4 which concerns de Moivre's theorem and its applications. But I am stuck on the last problem.

Could someone look at the last problem in Chapter 4 and give me some help? Preferably a small hint, NOT the whole solution. Here is the book: http://filestore.aqa.org.uk/subjects...2-TEXTBOOK.PDF
By the way it's the very last part I'm stuck on; I managed the rest of the question fine.

I want to know the most elegant/quickest method if possible. Thanks.
Which question exactly, and can't you screenshot the question (or use the snipping tool in Win7/8 and save the image)?
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PrimeLime
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(Original post by kkboyk)
Which question exactly, and can't you screenshot the question (or use the snipping tool in Win7/8 and save the image)?
The very last part question of Chapter 4. The one with w, alpha, beta, gamma, the squares, modulus sign all equal to 6, etc.
It's much easier to just paste the URL. Should be quite easy to find.
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kkboyk
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(Original post by PrimeLime)
The very last part question of Chapter 4. The one with w, alpha, beta, gamma, the squares, modulus sign all equal to 6, etc.
It's much easier to just paste the URL. Should be quite easy to find.
Hmm that's interesting. It might take me a long time to come up with some different solutions
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PrimeLime
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(Original post by kkboyk)
Hmm that's interesting. It might take me a long time to come up with some different solutions
It is isn't it? Didn't think A-Level Maths/FM got that interesting/challenging XD.
Got any solutions yet? So far I've only been able to come up with idiotic ideas...
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DFranklin
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(Original post by PrimeLime)
It is isn't it? Didn't think A-Level Maths/FM got that interesting/challenging XD.
Got any solutions yet? So far I've only been able to come up with idiotic ideas...
I think if you simply expand out the LHS and think about the values of \alpha+\beta+\gamma and \alpha^2+\beta^2+\gamma^2 it comes out OK.
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PrimeLime
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(Original post by DFranklin)
I think if you simply expand out the LHS and think about the values of \alpha+\beta+\gamma and \alpha^2+\beta^2+\gamma^2 it comes out OK.
Oh of course I'm so stupid. I considered the expansion since I noticed that the modulus of w^2 must be 2 and so 3w^2 was 6 but didn't notice the fact that the symmetric sums of those roots were clearly 0...
Thanks for your hint .
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PrimeLime
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Anyone got any clever geometric proofs of this?
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