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    Hi,

    I am struggling to make any further progression with question 6 (a).

    I have made Z the subject, taken the modulus of both sides and ended up with:

     3 = \frac{|iw|}{|1-w|}

    However, I don't know what to do here. I've tried substituting w = u + iv into there, but when I square both sides to remove the moduli, it becomes a mess with lots of i terms, which I don't know how to deal with. The mark scheme says something about using Pythagoras, but I'm not entirely sure how that is relevant here?



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    (Original post by kingaaran)
    Hi,

    I am struggling to make any further progression with question 6 (a).

    I have made Z the subject, taken the modulus of both sides and ended up with:

     3 = \frac{|iw|}{|1-w|}

    However, I don't know what to do here. I've tried substituting w = u + iv into there, but when I square both sides to remove the moduli, it becomes a mess with lots of i terms, which I don't know how to deal with. The mark scheme says something about using Pythagoras, but I'm not entirely sure how that is relevant here?



    Name:  ImageUploadedByStudent Room1421702631.180948.jpg
Views: 232
Size:  76.8 KB




    Posted from TSR Mobile
    • multiply across
    • use w = u + iv
    • group real and imaginary
    • use definition of modulus
    • square both sides
    • simplify
    • complete squares
    • read circle particulars
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    (Original post by TeeEm)
    • multiply across
    • use w = u + iv
    • group real and imaginary
    • use definition of modulus
    • square both sides
    • simplify
    • complete squares
    • read circle particulars
    What do you mean by 'use definition of modulus'?


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    (Original post by kingaaran)
    What do you mean by 'use definition of modulus'?


    Posted from TSR Mobile
    |a+bi|=√(a2+b2)
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    (Original post by TeeEm)
    |a+bi|=√(a2+b2)
    THANK YOU SO MUCH


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    (Original post by kingaaran)
    THANK YOU SO MUCH


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    my pleasure
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    (Original post by TeeEm)
    my pleasure

    One question - how did the mark scheme get (u-1)^2 - got (1-u)^2. I'm assuming they took -1 out of the modulus, but would that make a difference to the answer?


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    (Original post by kingaaran)
    One question - how did the mark scheme get (u-1)^2 - got (1-u)^2. I'm assuming they took -1 out of the modulus, but would that make a difference to the answer?


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    no difference

    should be obvious by expanding that (u-1)2 = (1-u)2
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    (Original post by TeeEm)
    no difference

    should be obvious by expanding that (u-1)2 = (1-u)2
    Oh yeah, I'm so silly haha! Thanks though


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    (Original post by kingaaran)
    Oh yeah, I'm so silly haha! Thanks though


    Posted from TSR Mobile
    no worries
 
 
 
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