\begin{align*}
 c &:= a + i*b \\
 f_c &: \mathbb{C} \mapsto \mathbb{C} \\
 f_c(c + i*d) &:= (c^2 - d^2 + a) + i*(2 * c * d + b)
\end{align*}

http://quicklatex.com/