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Let `A_(1), A_(2)…….A_(7)` be a polygon and `a(1), a_(2)……a_(7)` be the complex numbers representing vertices `A_(1), A_(2)……A_(7)`. If `|a_(1)|=|a_(2)|=……….|a_(7)=R`, then `sum_(1le i lt j le 7)|a_(i)+a_(j)|^(2)`A. greater than `30R^(2)`B. has minimum value as `35R^(2)`C. has its minimum value in `(25R^(2),45R^(2))`D. is less than `45R^(2)` |
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Answer» Correct Answer - A::B::C `(sum_1le i lt j le7)|a_(i)+a_(j)|^(2)=sum_(1le i lt j le 7)(|a_(i)|^(2)+|a_(j)|^(2)+a_(i)bara_(j)+bara_(i)a_(j))` `=2R^(2.7)C_(2)+sum_(i!=j)a_(i)bara_(j)=42R^(2)+sum_(i=1)^(7) sum_(j=1)^(7) a_(i)bara_(j)-sum_(i=1)^(7)a_(i)bara_(i)` `=35R^(2)+(sum_(i=1)^(7)a_(i))(sum_(i=1)^(7)bara_(i))-7R^(2)` `=35R^(2)+|sum_(i=1)^(7)a_(i)|^(2)ge 35R^(2)` |
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