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# 10.3 - 1 1 1 1 1 i i 2 i 3 1 i 2 i 4 i 6 1 i 3 i 6 i 9 = 1...

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Math 2940 Solutions, Fall 2011 Section 10 . 3 1 ) 1 1 1 i 1 - 1 1 - i 1 1 1 i 2 1 1 1 i 2 1 1 1 1 = 1 1 1 1 1 i 2 i - i 1 1 - 1 - 1 1 i 2 - i i 1 1 1 1 = 1 1 1 1 1 i i 2 i 3 1 i 2 i 4 i 6 1 i 3 i 6 i 9 . That i 2 = - 1 is used in a bunch of places. 3 ) F = 1 1 1 1 1 1 1 i 2 1 1 1 i 2 1 1 1 1 1 - 1 i - i . 4 ) D = 1 0 0 0 e 2 πi/ 6 0 0 0 e 4 πi/ 6 , F 3 = 1 1 1 1 e 2 πi/ 3 e 4 πi/ 3 1 e 4 πi/ 3 e 2 πi/ 3 , P = 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 . So F 6 = I D I - D F 3 F 3 [ P ]. 6 ) 1 1 1 1 1 i i 2 i 3 1 i 2 i 4 i 6 1 i 3 i 6 i 9 2 = 4 0 0 0 0 0 0 4 0 0 4 0 0 4 0 0 . Squaring again, we get 16 I . 11 ) 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0
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Unformatted text preview: 1 1 1 1 1 i i 2 i 3 1 i 2 i 4 i 6 1 i 3 i 6 i 9 = 1 1 1 1 1 i i 2 i 3 1 i 2 i 4 i 6 1 i 3 i 6 i 9 1 i i 2 i 3 ....
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