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Ifz_(1),z_(2),z_(3) are three points lying on the circle |z|=2, then minimum value of |z_(1)+z_(2)|^(2)+|z_(2)+z_(3)|^(2)+|z_(3)+z_(1)|^(2)=

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Solution :`|z|=|z_(2)|=|z_(3)|=2`
`because |z_(1)+z_(2)+z_(3)|^(2)ge0implies(z_(1)+z_(2)+z_(3))(barz_(1)+barz_(2)+barz_3)GE0`
`impliessum|z_(1)|^(2)+sum(z_(1)barz_(2)+barz_(1)z_(2))ge0implies2sum|z_(1)|^(2)+sum(z_(1)barz_(2)+barz_(1)z_(2))gesum|z_(1)|^(2)`
`implies|z_(1)+z_(2)|^(2)+|z_(2)+z_(3)|^(2)+|z_(3)+z_(1)|^(2)GE12 {because |z_(1)|=|z_(2)|=|z_(3)|=2}`


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