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Complex inequality with absolute values

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine the values of [itex] z \in \mathbb{C} [/itex] for which [itex]|z+2| > 1 + |z-2| [/itex] holds.

    2. Relevant equations

    Nothing complicated I can think of.

    3. The attempt at a solution

    For real values this holds for anything greater than [itex]1/2[/itex]. If I could figure out the boundaries of the area I'd be set, but the triangle inequality doesn't return anything nontrivial here. Tedious expansion into real and imaginary terms could be a solution, but there's probably a better way.
     
  2. jcsd
  3. Oct 19, 2011 #2
    I've found out through wolfram alpha that the inequality holds for an area enclosed by two crossing lines. Not quite sure where to get the two lines from
     
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