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Math Help - Describe the locus

  1. #1
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    Describe the locus

    I'm not sure about this problem (see attachment) as I haven't come across one with a lower constaint. I think it just means the locus can't be below 0. If that's the case then I think I've done it correctly, but I have posted my working (see attachment) just to be sure.

    Thanks, Daddy_Long_Legs
    Attached Thumbnails Attached Thumbnails Describe the locus-question-3.jpg   Describe the locus-question-3-working.jpg  
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  2. #2
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    the modulus is equivalent to the length so it must be positive
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  3. #3
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    I'm not sure what you mean by that, does that mean I've done it right?
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  4. #4
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    Quote Originally Posted by Daddy_Long_Legs View Post
    I'm not sure what you mean by that, does that mean I've done it right?
    The solution is all values of z inside the circle you found, except for z = -i.
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  5. #5
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    mr fantastic,

    The question only asks to describe the locus, not find any solutions of z. I'm assuming the circle I have found is correct?
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  6. #6
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    Hi Daddy_Long_Legs

    Yes, your circle is correct. And when you describe the locus, you should pay attention to what mr fantastic has said

    The solution is all values of z inside the circle you found, except for z = -i
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  7. #7
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    songoku and mr fantastic,

    I haven't usually gone into that much detail when describing the locus. What I essentially put is all I needed for my exercises.
    Last edited by Daddy_Long_Legs; August 12th 2009 at 08:18 PM.
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  8. #8
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    Quote Originally Posted by Daddy_Long_Legs View Post
    mr fantastic,

    The question only asks to describe the locus, not find any solutions of z. I'm assuming the circle I have found is correct?
    |z + i| = 2 defines a locus (the circle you found).

    However .... 0 < | z + i| < 2 does not define a locus, it defines a region. The region is a punctured disk, described in my earlier post.
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  9. #9
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    mr fantastic,

    That is why I say the interior of the circle, centred at (0,-1) with radius 2. Not just the circle centred at (0,-1) with radius 2.
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  10. #10
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    Quote Originally Posted by Daddy_Long_Legs View Post
    mr fantastic,

    That is why I say the interior of the circle, centred at (0,-1) with radius 2. Not just the circle centred at (0,-1) with radius 2.
    But it's not the entire interior ..... z = -i (the centre) is excluded.
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  11. #11
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    mr fantastic,

    I’m not sure how you found that the locus can not be equal to z=-i, if it has to do with the fact that 0<, and then it can’t equal –i, this was my original question, as I wasn’t sure about this. This just means then, the locus is the interior of the circle, centred at (0,-1) with radius 2 excluding z=-i. Is this correct?
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  12. #12
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    Quote Originally Posted by Daddy_Long_Legs View Post
    mr fantastic,

    Iím not sure how you found that the locus can not be equal to z=-i, if it has to do with the fact that 0<, and then it canít equal Ėi, Mr F says: Correct.

    this was my original question, as I wasnít sure about this. This just means then, the locus is the interior of the circle, centred at (0,-1) with radius 2 excluding z=-i. Is this correct? Mr F says: Yes.
    ..
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  13. #13
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    Okay, mr fantastic, got it, thanks for the help.
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