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Let z1,z2,z3 are three pair wise distin...

Let `z_1,z_2,z_3` are three pair wise distinct complex numbers and `t_1,t_2,t_3` are non-negative real numbers such that `t_1+t_2 +t_3 = 1`. Prove that the complex number `z=t_1z_1 +t_2z_2+t_3z_3` lies inside a triangle with vertices `z_1, z_2, z_3` or on its boundary.

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