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Unformatted text preview: Let = e 2 i/ 5 . (i) SHOW that 1 + + 2 + 3 + 4 = 0. HINT. Expand (1 )(1 + + 2 + 3 + 4 ), and use the fact that 5 = 1. (ii) SHOW that + 4 = 2cos 2 5 . HINT. Remember that cos(2  ) = cos( ) and sin(2  ) =sin( ). (iii) SHOW that 2 + 3 = ( + 4 ) 22. (iv) Hence SHOW that x = 2cos 2 5 is a root of the polynomial x 2 + x1 = 0 , and that cos 2 5 = 51 4 . 1...
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 Spring '08
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