Unformatted text preview: a 1 ≤ a 2 ≤ a 3 ≤ ··· , where a n = ± 1 + 1 n ¶ n . Hint. Consider a n /a n1 . #5. Represent z 4 + 4 in the form z 4 + 4 = ( zz )( zz 1 )( zz 2 )( zz 3 ) with ﬁxed complex numbers z k , and also as a product of two quadratic polynomials with real coeﬃcients. 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 iθ = r (cos θ + i sin θ ) with r > has n distinct solutions z k = r 1 /n e i ( θ +2 kπ ) /n , where k = 0 , 1 , 2 ,...,n1 ....
View
Full Document
 Fall '09
 Math, Math 5615H, different solutions solutions

Click to edit the document details