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Homework Help: Checking the answer to complex number question

  1. Sep 20, 2008 #1

    rock.freak667

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    1. The problem statement, all variables and given/known data
    Find an equation connecting x and y for which (z-1)/(z+1) has an argument [itex]\alpha[/itex]


    2. Relevant equations
    z=x+iy

    arg(z)=tan-1(y/x)


    3. The attempt at a solution

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

    Substituting z=x+iy

    [tex]\Rightarrow \frac{z-1}{z+1}=\frac{(x-1)+iy}{(x+1)+iy}[/tex]

    Realizing

    [tex]\frac{(x+1)(x-1)+iy(x+1)-iy(x-1)-i^2y^2}{(x+1)^2+y^2}[/tex]

    Re:i2=-1

    [tex]= \frac{x^2+y^2-1}{(x+1)^2+y^2} +i \frac{2y}{(x+1)^2+y^2}[/tex]

    Thus

    [tex]tan\alpha = \frac{2y}{x^2+y^2-1}[/tex]

    Is this correct? Or should I just put in the form of a circle?
     
  2. jcsd
  3. Sep 20, 2008 #2

    tiny-tim

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    Hi rock.freak667! :smile:

    Yes, that's messy! :biggrin:

    Definitely put it in the form of a nice circle (x² + (y-a)² = b²)! :wink:
     
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