Complex number geometry

Geometry Level 5

Let z1,z2,z_1, z_2, and z3z_3 be complex numbers satisfying zi3=1|z-i\sqrt{3}|=1 and 3z1+i3=2z2+2z33z_{1}+i\sqrt{3}=2z_{2}+2z_{3}.

Find z1z2\large{|z_{1}-z_{2}|}

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