1. Given $z_{1}, z_{2}$ are complex numbers, and satisfy $\left|z_{1}\right|=\left|z_{2}\right|=\left|z_{1}-z_{2}\right|=1$, then $\left|z_{1}+z_{2}\right|=$
$$
\left|z_{1}+z_{2}\right|^{2}+\left|z_{1}-z_{2}\right|^{2}=2\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right)=4 \Rightarrow\left|z_{1}+z_{2}\right|=\sqrt{3}
$$

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$$
\left|z_{1}+z_{2}\right|^{2}+\left|z_{1}-z_{2}\right|^{2}=2\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right)=4 \Rightarrow\left|z_{1}+z_{2}\right|=\sqrt{3}
$$