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Let z1,z2,z_1, z_2,z1,z2, and z3z_3z3 be complex numbers satisfying ∣z−i3∣=1|z-i\sqrt{3}|=1∣z−i3∣=1 and 3z1+i3=2z2+2z33z_{1}+i\sqrt{3}=2z_{2}+2z_{3}3z1+i3=2z2+2z3.
Find ∣z1−z2∣\large{|z_{1}-z_{2}|}∣z1−z2∣
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