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Complex Numbers Locus Question

  1. Nov 30, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the cartesian equation of the locus |z+3+2i|=Re(z)


    2. Relevant equations



    3. The attempt at a solution
    You let z= x +iy
    therefore Re(z)=x?
     
  2. jcsd
  3. Nov 30, 2009 #2

    Hootenanny

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    Indeed. So you now have

    [tex] x = \left| x + 3 +iy + 2i\right|[/tex]

    Can you write that in canonical form?
     
  4. Nov 30, 2009 #3
    OK. I'm not too sure what you mean by canonical form?
    Would x = {(x+3)^2 + (y+2)^2}^1/2
    Therefore: x^2 = x^2 +6x + 9 +y^2 +4y+4
    6x+4y+y^2=-13
    I'm not quite sure what to do now
    Thanks for the help
     
  5. Nov 30, 2009 #4

    Hootenanny

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    You're there. The canonical form in Cartesian coordinates is usually f(x,y) = 0 or f(x,y) = const., which is what you have there.
     
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