Assume that \( A_{\mathrm{i}}(i=1,2, \ldots, n) \) are the vertices of a regular polygon inscrib...

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Assume that \( A_{\mathrm{i}}(i=1,2, \ldots, n) \) are the vertices of a regular polygon inscribed in a circle of radius unity. Find
(i) \( \left|A_{1} A_{2}\right|^{2}+\left|A_{1} A_{3}\right|^{2}+\ldots+\left|A_{1} A_{n}\right|^{2} \)
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