(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define L: |z| = 1 -----> Re( (1 + w)) = 0. Find L.

2. Relevant equations

A transformation is defined by three unique points by T(z) = (z-z1)(z2-z3) / (z-z3)(z2-z1). If we have two transformations T and S, and we want T = S for three distinct points, then we have the transformation L by the transformation S^(-1)[T(z)].

3. The attempt at a solution

I chose the points on the circle 1, i, and -1 to go to the points infinity, 0 and 1+i respectively. My calculations gave me L(z) = (1+i)((z-i) - (z+1))(infinity) / ((infinity)(z-1)i - (z+1)(1+i)). The book gives me u(1-i)(z+1)/(z-1) where u is any real number.

What should I do to get this simple form (aka the right answer). Thank you.

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

2. Relevant equations

3. The attempt at a solution

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

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Find a linear fractional transformation that carries circle to a line.

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