Year 13 Maths Help Thread

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Four things that unis think matter more than league tables 08-12-2016
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    (Original post by Ayman!)
    Better not post it here - the TSR police will arrest me. :mob:

    Check your PM soon, I'm looking for the link :lol:
    Aye aye. Local bookshop only stocks stuff that are usable for just maths, not so much for FM ;-;
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    (Original post by Imperion)
    Aye aye. Local bookshop only stocks stuff that are usable for just maths, not so much for FM ;-;
    There used to be a school website who had them all, the website is no longer up, I've got the livetext for each book but none that are just the PDF themselves


    edit: if anyone has the pdf msg me it :P
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    (Original post by metrize)
    There used to be a school website who had them all, the website is no longer up, I've got the livetext for each book but none that are just the PDF themselves


    edit: if anyone has the pdf msg me it :P
    Tbf I wouldn't mind livetext either
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    Shall I PM you the modules I'm interested in?
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    I'll have to insist that the above discussion about infringing copyright will have to stop.
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    :security:
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    (Original post by SeanFM)
    :security:
    :elefant:
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    All in the best interest of education.
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    Prove that  \displaystyle \sqrt[4]{\frac{1}{2}(1+ i\sqrt 3 )} + \sqrt[4]{\frac{1}{2}(1-i \sqrt 3)}\equiv \sqrt[3]{\frac{1}{2}\sqrt 2 (1+i)} + \sqrt[3]{\frac{1}{2}\sqrt 2 (1-i)}.

    Is this really easy for a FM question?
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    (Original post by Ano123)
    Prove that  \displaystyle \sqrt[4]{\frac{1}{2}(1+ i\sqrt 3 )} \equiv \sqrt[3]{\frac{1}{2}\sqrt 2 (1+i)}.

    Is this really easy for a FM question?
    Yes.
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    (Original post by Ano123)
    Is this really easy for a FM question?
    Doesn't make sense, there isn't really a thing as a principal root for n-th roots where n > 2 in the complexes, so for example, the LHS has 4 fourth roots whilst the RHS has 3 third roots and you're claiming the two are equivalent.
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    (Original post by Zacken)
    Doesn't make sense, there isn't really a thing as a principal root for n-th roots where n > 2 in the complexes, so for example, the LHS has 4 fourth roots whilst the RHS has 3 third roots and you're claiming the two are equivalent.
    I've tried to edit it because it's not fully what I mean to put. I will try and edit it in a minute again.
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    (Original post by RDKGames)
    Yes.
    I've edited it now.
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    (Original post by Ano123)
    I've edited it now.
    That's still straight forward. Maybe it's just me, never had a problem with roots of unity in FM. The only thing to do here is to convert it into re^{i\theta} form, factor out indices and maybe draw yourself a complex plane so there isn't much challenge.
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    (Original post by RDKGames)
    That's still straight forward. Maybe it's just me, never had a problem with roots of unity in FM. The only thing to do here is to convert it into re^{i\theta} form so there isn't much challenge.
    I just play around with a few concepts and see if I can make any interesting questions from it. Obviously not here.
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    (Original post by Ano123)
    I just play around with a few concepts and see if I can make any interesting questions from it. Obviously not here.
    Try linking these types to De Moivre's perhaps? Those can sometimes be challenging and can lead onto roots of polynomials.
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    (Original post by RDKGames)
    Try linking these types to De Moivre's perhaps? Those can sometimes be challenging and can lead onto roots of polynomials.
    Yeah. I like those questions. Let me see what I can come up with.
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    Bleurgh, no. All these are boring and tedious questions. For a given complex number a, call a a primitive nth root of unity if and only if a^n = 1 and there is no integer m such that a^m = 1 where 0< m < n.

    Let C_n(x) be the (cyclotomic) polynomial such that the roots of the equations of C_n are the primitive nth roots of unity, the coefficient of the highest power of x is 1 and all roots have multiplicity 1.

    Find C_p(x) where p is a given prime and prove that there are no positive integers q,r and s such that C_q(x) \equiv C_r(x)C_s(x).
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    (Original post by Zacken)
    Bleurgh, no. All these are boring and tedious questions. For a given complex number a, call a a primitive nth root of unity if and only if a^n = 1 and there is no integer m such that a^m = 1 where 0< m < n.

    Let C_n(x) be the (cyclotomic) polynomial such that the roots of the equations of C_n are the primitive nth roots of unity, the coefficient of the highest power of x is 1 and all roots have multiplicity 1.

    Find C_p(x) where p is a given prime and prove that there are no positive integers q,r and s such that C_q(x) \equiv C_r(x)C_s(x).
    No thanks. I don't think many Y13's will know what to do here lol
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    What would a graph of x^x look like when x \leq 0?

    Secondly, what is lim_{x->-\infty} x^x (apologies for the TeX)?
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    (Original post by Palette)
    What would a graph of x^x look like when x \leq 0?

    Secondly, what is lim_{x->-\infty} x^x (apologies for the TeX)?
    1. You cant draw it in the real plane.

    2. Limit does not exist by continuity
 
 
 
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