1. Given $z_{1}, z_{2}$ correspond to points $P, Q$ on the complex plane, and $\left|z_{2}\right|=4,4 z_{1}^{2}-2 z_{1} z_{2}+z_{2}^{2}=0$. Then the area of $\triangle O P Q$ formed by $P, Q$ and the origin $O$ is equal to
$$
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\therefore\left|z_{1}\right|=\left|\frac{1 \pm \sqrt{3} i}{4}\right| \cdot\left|z_{2}\right|=2 . \text { and } \\
\arg \left(\frac{z_{1}}{z_{2}}\right)=\arg \frac{1 \pm \sqrt{3} i}{4}= \pm \frac{\pi}{3} . \therefore \angle P O Q=\frac{\pi}{3} . \\
\text { Therefore, } S_{\triangle O P Q}=\frac{1}{2}\left|z_{1}\right| \cdot\left|z_{2}\right| \cdot \sin \frac{\pi}{3}=2 \sqrt{3} .
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$$