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If `z_(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)=`A. 6B. 12C. 15D. 24 |
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Answer» Correct Answer - B `|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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