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Complex Numbers Geometry

  1. Feb 8, 2007 #1
    1. The problem statement, all variables and given/known data
    Describe the locus of points z satisfying the given equation.

    2. Relevant equations

    3. The attempt at a solution
    I started on the second one:
    I think that Re(z) is just x, then
    I squared both sides, simplified and got

    (y-1)^2=0 is this correct? If so how would I go about the Im(2iz) LHS on the first equation?

    Thank you
  2. jcsd
  3. Feb 9, 2007 #2


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    That's the right way to start, but you are not quite done yet.

    When you squared the equation, you found the solutions of

    |z-i| = +Re(z) or |z-i| = -Re(z).

    Draw a picture of your solution (y-1)^2 = 0 on an Argand diagram to see what part of it corresponds to |z-i| = +Re(z)

    Let z = x + iy, then work out what is the imaginary part of (2iz).
    Last edited: Feb 9, 2007
  4. Feb 9, 2007 #3


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    And if (y-1)2= 0, what can you say about y?

    Pretty much the same thing. Let z= x+iy. What is 2iz in terms of x and y? What is Im(2iz)?
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