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Unformatted text preview: a 1 a 2 a 3 , where a n = 1 + 1 n n . Hint. Consider a n /a n-1 . #5. Represent z 4 + 4 in the form z 4 + 4 = ( z-z )( z-z 1 )( z-z 2 )( z-z 3 ) with xed complex numbers z k , and also as a product of two quadratic polynomials with real coecients. Hint. Here z k are distinct complex roots of the polynomial z 4 + 4, or equivalently, solutions of the equation z 4 =-4. In general, z n = w = r e i = r (cos + i sin ) with r > has n distinct solutions z k = r 1 /n e i ( +2 k ) /n , where k = 0 , 1 , 2 ,...,n-1 ....
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This document was uploaded on 02/15/2012.
- Fall '09