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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) |
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Answer» greater than `30R^(2)` `=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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