# Complex number geometry

Geometry Level 5

Let $$z_1, z_2,$$ and $$z_3$$ be complex numbers satisfying $$|z-i\sqrt{3}|=1$$ and $$3z_{1}+i\sqrt{3}=2z_{2}+2z_{3}$$.

Find $$\large{|z_{1}-z_{2}|}$$

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