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Identify and sketch the region in the complex plane satisfying

  1. Jul 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Identify and sketch the region in the complex plane satisfying

    [tex]
    | \frac{2 z - 1}{z + i} | \geq 1
    [/tex]

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 25, 2009 #2

    HallsofIvy

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    Staff Emeritus
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    Geometrically, |z- a| is the distance from z to a as points in the complex plane so I recommend you try to rewrite the given absolute value in that way. It might help to "rationalize the denominator", multiplying both numerator and denominator by z- i.
     
  4. Feb 26, 2010 #3
    Let z=x+yi. Now simplify your inequality by: |2z-1| greater than or equal to |z+i|.(multiply out |z+i|). sub z=x+yi into this inequality. You will find that it gives a circle (if not its an ellipse, i may have made a quick error in attempting to answer this). The area outside this graph is your answer.
     
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