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Thread: BOS trial

  1. #1
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    BOS trial

    Was stuck on a question:
    Sketch the locus defined by arg(z^2+z)=pi/3, stating its equation.
    Obviously this will turn into the hyperbola with the positive branch, but how do we find the equation?

    Also, anyone know when the bored of studies trial will be held this year, of is it held already?

    Thanks in advanced!

  2. #2
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    Re: BOS trial

    ive never seen this questions before; but this is how i would solve it. How is it "obviously" a hyperbola btw?
    argz+argz+1=pi/3
    take tan of both sides, or sin or cos or whatever i dont think it matters
    for tan actually: tan(a(z+1)+a(z))= sqr3
    tan(arg(z))=Im/Re=y/x
    tan(arg(z+1))=y/x+1
    let tan(arg(z+1))=a and tan(arg z) = b

    we have a+b/(1-ab)=sqr3 (angle formula)
    (y/x+y/(x+1)) / (1-y^2/(x^2+x))=3^0.5
    just manipulate and u should get an answer; im pretty sure this is incorrect but meh. It gives a shape that looks like at tilted hyperbola btw.

    what's the bos trial?
    Last edited by mrbunton; 30 Aug 2018 at 11:55 PM.

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    -insert title here- Paradoxica's Avatar
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    Re: BOS trial

    Quote Originally Posted by mrbunton View Post
    what's the bos trial?
    ban
    jathu123 likes this.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: BOS trial

    If

    ,

    then



    But since ,



    also gives the locus of .

    To get around this we can require to be in the first quadrant, i.e. and .

    Setting , this gives:

    Last edited by fan96; 31 Aug 2018 at 1:02 AM.

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    Re: BOS trial

    Quote Originally Posted by Paradoxica View Post
    ban
    what? is that banned?

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    -insert title here- Paradoxica's Avatar
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    Re: BOS trial

    Quote Originally Posted by mathsbrain View Post
    what? is that banned?
    whoosh

    was a joke my dude
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    The pessimistic optimist. BLIT2014's Avatar
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    Re: BOS trial

    BOS trial typically gets held later this year closer to HSC so it has not already been done.
    l’appel du vide


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    Re: BOS trial

    Thanks for the fun!

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    Re: BOS trial

    Quote Originally Posted by mathsbrain View Post
    Also, anyone know when the bored of studies trial will be held this year, of is it held already?
    There are plans underway to hold them this year in early October. Stay tuned for more details.
    jathu123 likes this.

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