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Plot complex region

  1. Apr 17, 2010 #1
    1. The problem statement, all variables and given/known data
    i was supposed to figure out what this region looks like ad to plot it
    [tex] \left| \frac{z + i}{z - i} \right| > 1 [/tex]



    2. Relevant equations

    [itex] z = x + iy [/itex]


    3. The attempt at a solution

    i tried a couple of rearrangements but i got nowhere:
    [tex] \left|z+i \right| > \left| z - i \right| [/tex]
    getting:
    [tex] \sqrt{ x^2 + (y+1)^2 } > \sqrt{ x^2 + (y-1)^2 } [/tex]

    which ends up [tex] 4y > 0 [/tex]
    is this it? simply y>0?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 17, 2010 #2
    i think, im not sure, but try something like this

    |a| > |b|

    => a > |b| or a < -|b|

    => -a < b < a or a < b < -a

    => (b > -a and b < a ) or (b > a and b < -a)

    and plot
     
    Last edited: Apr 17, 2010
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