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Help with a complex mapping

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Let the Complex mapping
    z → f(z) =(1 + z)/(1 − z)
    1.What are the images of i and 1 − i and 2.What are the images of the real and the imaginary axes?




    3. The attempt at a solution
    For i we have f(i)=(1+i)/(1-i) since i(depending on the power) can be i,-i,1,-1=>0, (1+i)/(1-i),(1-i)/(1+i)
    For 1 − i we have 1,-3,(2-i)/i,(2+i)/i.
    Not sure about the second part..
     
  2. jcsd
  3. Feb 6, 2012 #2

    vela

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    I'm not sure why you're looking at the various powers of i. It only appears to the first power in your expression. Use the following method to simplify it:
    $$f(i) = \frac{1+i}{1-i} = \frac{1+i}{1-i}\cdot\frac{1+i}{1+i} = \ ?$$
     
  4. Feb 6, 2012 #3
    Sorry I was tired,thanks for the reply..how should I think about the both parts of the problem.?..Also.I"m getting -1 for f(i)
     
  5. Feb 6, 2012 #4

    vela

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    That's still wrong. You should find f(i)=i.

    If z=x+iy is a point on the imaginary axis, you know that x=0, so you want to find f(z)=f(iy). Can you take it from there?
     
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