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If |z(1)|= |z(2)|= ….= |z(n)|=1, prove t...

If `|z_(1)|= |z_(2)|= ….= |z_(n)|=1`, prove that `|z_(1) + z_(2) + …+ z_(n)|= |(1)/(z_(1)) + (1)/(z_(2)) + …(1)/(z_(n))|`

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