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Math Help - Linear Transformation

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    3

    Linear Transformation

    Hello,

    I'm trying to find the linear fractional transformation that maps points
    z1 = -i, z2 = 0, z3 = i onto points w1 = -1, w2 = i, w3 = 1.

    I have set it up using the form:

    (w-w1)(w2-w3) / (w-w3)(w2-w1) = (z-z1)(z2-z3) / (z-z3)(z2-z1) such that in my example (w+1)(i-1) / (w-1)(i+1) = (z+i)(0-i) / (z-i)(i).

    Multiplying the left side by (i-1) / (i -1), I have i[(w+1) / (w-1)] = the right side of the equation above.

    Getting rid of the i on the left side, I have (w+1)/(w-1) = i[(z+i)/(z-i)].

    I'm stuck at the point where I have: (w+1)(z-i) = (-iz - 1)(w-1). Is this correct, and what do the final steps look like from here?

    Thank you.
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  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    I got
    \frac{w+1}{w-1}=i \frac{z+i}{z-i}=\frac{zi-1}{z-i}
    Expressing w
    w=i \frac{1-z}{1+z}
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