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

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

So your equation should look like this :

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

to remove the numbering of the first line.