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Complex Numbershard
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Let z1,z2,z3z_1, z_2, z_3z1​,z2​,z3​ be complex numbers such that ∣z1∣=∣z2∣=∣z3∣=1|z_1|=|z_2|=|z_3|=1∣z1​∣=∣z2​∣=∣z3​∣=1 and z1+z2+z3=0z_1+z_2+z_3=0z1​+z2​+z3​=0. What is z12+z22+z32z_1^2 + z_2^2 + z_3^2z12​+z22​+z32​?