Simple check of Fagnano identity via Euler's identity, with Latex ("chktex"ed)

fagnano.tex

\documentclass{article}
\begin{document}

\begin{eqnarray*}
 Fagnano: \pi& =& 2 i \log\frac{1-i}{1+i} \\
             &  & \\
   Euler: -1 & =&  e^{i \pi} \\
             & =&  e^{-2 \log\frac{1-i}{1+i} } \\
             & =&  \left(\frac{1-i}{1+i}\right) ^ {-2} \\
             & =&  \left({\frac{1+i}{1-i}}\right) ^ 2 \\
             &  & \\
  -{(1-i)^2} & =& (1+i) ^ 2 \\
 -1+2i-{i^2} & =& 1+2i+i^2 \\
          -2 & =& 2i^2
\end{eqnarray*}

\end{document}