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.
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