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If z1 + z2 + z3 + z4 = 0 where bi in ...

If `z_1 + z_2 + z_3 + z_4 = 0` where `b_i in R` such that the sum of no two values being zero and `b_1 z_1+b_2z_2 +b_3z_3 + b_4z_4 = 0` where `z_1,z_2,z_3,z_4` are arbitrary complex numbers such that no three of them are collinear, prove that the four complex numbers would be concyclic if `|b_1b_2||z_1-z_2|^2=|b_3b_4||z_3-z_4|^2`.

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