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Complex locus 2

  1. Dec 12, 2008 #1

    Mentallic

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    1. The problem statement, all variables and given/known data
    If R is a real number, find the locus of z defined by:

    [tex]z=\frac{1+iR}{1-iR}[/tex]

    2. Relevant equations
    [tex]z=x+iy[/tex]

    3. The attempt at a solution
    [tex]z=(\frac{1+iR}{1-iR})(\frac{1+iR}{1+iR})[/tex]

    [tex]=\frac{1-R^2+i2R}{1+R^2}[/tex]

    Therefore, [tex]x=\frac{1-R^2}{1+R^2}[/tex]

    and [tex]y=\frac{2R}{1+R^2}[/tex]

    I'm unsure what to do now though...
     
  2. jcsd
  3. Dec 12, 2008 #2

    gabbagabbahey

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    Hmmm... why not compute [tex]|z|[/tex] and see if that gives you anything useful:wink:
     
  4. Dec 12, 2008 #3

    Mentallic

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    Everything just fell into place and [tex]|z|=1[/tex]. How did you know that would happen? lol
     
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