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Homework Help: Reduce to x+iy

  1. Feb 1, 2009 #1
    1. The problem statement, all variables and given/known data

    Reduce to x+iy
    [tex]\frac{1+z}{1-z}[/tex] where z=cos[tex]\theta[/tex]+isin[tex]\theta[/tex].

    2. Relevant equations



    3. The attempt at a solution
    [tex]\frac{1+z}{1-z}[/tex]
    Multiply by conjugate
    [tex]\frac{1+2z+z^{2}}{1-z^{2}}[/tex]
    When I plug in the z value nothing seems to cancel out.
     
  2. jcsd
  3. Feb 1, 2009 #2

    gabbagabbahey

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    You seem to have multiplied both the numerator and denominator by [itex](1+z)[/itex]....but that isn't really the complex conjugate of [itex](1-z)[/itex] is it?:wink:....Don't you actually want to multiply by [itex](1-\bar{z})[/itex] instead?
     
  4. Feb 2, 2009 #3
    So i should multiply by 1+(costheta+isintheta)?
     
  5. Feb 2, 2009 #4

    gabbagabbahey

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    No, [itex]1-z=(1-\cos\theta)-i\sin\theta[/itex], so [itex]\overline{1-z}=[/itex]___?
     
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