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

Let `z_1, z_2, z_3` be three complex numbers and `a ,b ,c` be real numbers not all zero, such that `a+b+c=0` and `a z_1+b z_2+c z_3=0.` Show that `z_1, z_2,z_3` are collinear.

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