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Number of points having integral coordinates

  1. Oct 15, 2012 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    Let A,B,C be three sets of complex numbers as defined below

    A = {z:|z+1|[itex]\leq[/itex]2+Re(z)}, B = {z:|z-1|[itex]\geq[/itex]1} and
    C=[itex]\left\{z: \frac{|z-1|}{|z+1|}\geq 1 \right\}[/itex]

    The number of point(s) having integral coordinates in the region [itex]A \cap B \cap C[/itex] is

    2. Relevant equations

    3. The attempt at a solution
    I worked out and found that [itex]A \cap B \cap C[/itex] is the area bounded by the parabola [itex]y^{2}=2(x+\frac{3}{2})[/itex] and the Y-axis. So the points having integral coordinates in this region are (-1,0), (0,0), (-1,1) and (-1,-1) which counts up to 4. But the correct answer is 6.
     
  2. jcsd
  3. Oct 15, 2012 #2

    jambaugh

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    Get out a piece of graph paper and carefully graph your region. Note that boundary points are included in the given regions.
     
  4. Oct 15, 2012 #3

    utkarshakash

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    Ughhh... How can I miss (0,-1) and (0,1)! Thanks.
     
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