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Help on complex analysis(locus of z)

  1. Apr 4, 2014 #1
    1. The problem statement, all variables and given/known data.

    if z =x+yi.
    Determine the equation of the locus z in terms of x and y such that |(z+1)/(z-1)|=2

    3. The attempt at a solution.

    |(z+1)/(z-1)|=2

    (z+1)/(z-1)=2*2

    (x+yi+1)/(x+yi-1)=4

    [(x+1)+yi]/[(x-1)+yi]=4

    [(x+1)+yi]/[(x-1)+yi]×[(x-1)-yi]/[(x-1)-yi]=4

    [x*2-1-yi(x+1)+yi(x-1)-y*2i*2]/[(x-1)*2-yi(x-1)+yi(x-1)-y*2i*2]=4

    (x*2-1-xyi+xyi-yi-yi-y*2i*2)/(x*2-2x+1-xyi+xyi+yi-yi-y*2i*2)=4

    (x*2-1-2yi-y*2i*2)/(x*2-2x+1-y*2i*2)=4

    [x*2-1-2yi-y*2(-1)]/[x*2-2x+1-y*2(-1)]=4

    (x*2+y*2-1-2yi)/(x*2+y*2-2x+1)=4

    (x*2+y*2-1-2yi)=4(x*2+y*2-2x+1)

    x*2+y*2-1-2yi=4x*2+4y*2-8x+4

    3x*2+3y*2-8x+2yi+5=0
     
  2. jcsd
  3. Apr 4, 2014 #2

    BvU

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    Hello Stephen,

    modulus of a complex number is defined differently: | x+iy |2 = (x+iy)(x-iy) = x2+ y2
     
  4. Apr 4, 2014 #3

    PeroK

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    Wouldn't it be easier to start by multiplying by |z-1|?
     
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