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Let z1, z2, z3 be three distinct complex...

Let `z_1, z_2, z_3` be three distinct complex numbers satisfying `|z_1 - 1| = |z_2-1| = |z_3-1|`. Let A , B, and C be the points represented in the Argand plane corresponding to `z_1 , z_2 and z_3` respectively. Prove that `z_1 + z_2 + z_3=3` if and only if `Delta ABC` is an equilateral triangle.

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