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Describe complex set

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data
    Hey, hope that someone can be nice and help me describe this set:

    |z+2| < |z+2i|



    3. The attempt at a solution
    z = x + iy
    |z+2| < |z+2i|
    sqrt((x+2)^2 + y^2) < sqrt(x^2 + (y+2)^2)
    possible to do more?

    The left side is the equation for a circle with center x = -2, y = 0 and the right side is the equation for a circle with center x = 0 and y = -2.

    So the set is the circle described on the left side with radius less than the circle on the right side.
    Is this correct?
    And if I want to sketch the set?
     
  2. jcsd
  3. Sep 28, 2011 #2

    LCKurtz

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    Yes, it is possible to do more. Simplify it. Start by using the fact that if a and b are nonegative numbers and a < b, then a2<b2.
    No that isn't correct. Simplify it and look at the inequality you get and you will see how to graph it.
     
  4. Sep 28, 2011 #3
    Thanks for the help
    x + iy
    |z+2| < |z+2i|
    sqrt((x+2)^2 + y^2) < sqrt(x^2 + (y+2)^2)
    if a and b are nonegative numbers and a < b, then a2<b2
    (x+2)^2 + y^2 < x^2 + (y+2)^2
    x^2 + 4x +x + y^2 < x^2 + y^2 +4y + 4
    4x < 4y
    x < y

    sketch:
    divide the x,iy plate with x = y. The set is on the left side
     
  5. Sep 28, 2011 #4

    LCKurtz

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    Good. Hopefully that fits your intuition about what points are closer to -2 than to -2i.
     
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