LaTeX: Numbering only last line of multi-line equation in \align

From the amsmath documentatiom (amsldoc.pdf):

You can suppress the number on any
particular line by putting \notag
before the \\;

So your equation should look like this (some bits removed from your equation to make it shorter):

\begin{align}
z_1^2 &= \left( ... \right) \left( ... \right)\notag\\
&= 4 e^{i \frac{2 \pi}{3}}
\end{align}