\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
f (z)
 & = & (1 + i) z^{2} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
f (z)
 & = & (1 + i) z^{2} \\
& = & z^{2} + i z^{2} \\
& = & (x + iy) (x + iy) + i (x + iy) (x + iy) \\
& = & x^{2} + 2ixy - y^{2} + i (x^{2} + 2ixy - y^{2}) \\
& = & x^{2} + 2ixy - y^{2} + ix^{2} - 2xy - iy^{2} \\
& = & \underbrace{x^{2} - 2xy - y^{2}}_{u} + i \underbrace{(x^{2} + 2xy - y^{2})}_{v} \\
\end{eqnarray*}
\end{document}
