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Math Help - Subset of the complex plane

  1. #1
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    Subset of the complex plane

    I need help on another:

    |z-4-i|+|z+4+i| > 1
    Last edited by mr fantastic; February 21st 2009 at 03:16 PM.
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  2. #2
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    Looks like the "stuff" outside an ellipse.
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  3. #3
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    Quote Originally Posted by damo17 View Post
    I need help on another:

    |z-4-i|+|z+4+i| > 1
    First find |z - 4 - i| + |z + 4 + i| = 1 to get the boundary.

    Note that this can be written as |z - (4 + i)| + |z - (-4 - i)| = 1.

    Now ..... if you're familiar with the locus definition of an ellipse then there's a very simple way of seeing that there's no solution to this equation.

    Therefore the answer to the inequality is the entire complex plane ....
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  4. #4
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    Quote Originally Posted by manjohn12 View Post
    Looks like the "stuff" outside an ellipse.
    The equality does not define an ellipse because the distance between the focal points z = 4 + i and z = -4 - i is greater than 1 ....
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    The equality does not define an ellipse because the distance between the focal points z = 4 + i and z = -4 - i is greater than 1 ....

    So it is  \sqrt{68} > 1 . Oh okay. Was thinking the equality was equal to 10.
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  6. #6
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    Quote Originally Posted by damo17 View Post
    I need help on another:

    |z-4-i|+|z+4+i| > 1
    In your (unnecessary) re-posting of this question you said:

    Quote Originally Posted by damo17 View Post
    I need help on another question:

    |z-4-i|+|z+4+i| = 1

    [snip]
    So what's it meant to be then, an inequality or an equality? Either way, my first post contains the answer.

    If you need an algebraic approach where you substitute z = x + iy etc. please say so.
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  7. #7
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    Thanks,
    sorry for any confusion it's >1.
    I'm still confused a bit. Could you show working out by substituting z=x+yi in. Thanks
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