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Suppose the points z(1),z(2),…,z(n)(z(i)...

Suppose the points `z_(1),z_(2),…,z_(n)(z_(i) ne 0)` all lie on one side of a line drawn through the origin of the complex planes. Prove that the same is true of the points `1/z_(1),1/z_(2),...,1/z_(n)`. Moreover, show that `z_(1)+z_(2)+...+z_(n) ne 0 " and " 1/z_(1)+1/z_(2)+...+1/z_(n) ne 0`

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