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यदि omega इकाई का एक घनमूल हो, तो सारणिक...

यदि `omega` इकाई का एक घनमूल हो, तो सारणिक `|(1,omega^(4),omega^(8)),(omega^(4),omega^(8),1),(omega^(8),1,omega^(4))|` का मान है-

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(1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(5))(1-omega^(7))(1-omega^(8))

(1-omega+omega^(2))(1+omega-omega^(2))=4

(1+omega)(1+omega^(2))(1+omega^(3))(1+omega^(4))(1+omega^(5))......(1+omega^(3n))

(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-omega^(8)+omega^(16))

(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….. to 2n factors

Prove that (1-omega-omega^(2))(1-omega+omega^(2))(1+omega-omega^(2))=8

(1-omega +omega^2)(1+omega-omega^2)=4

(3 - omega) ( 3- omega^(2)) ( 3- omega^(4)) (3 - omega^(8)) =

(1 - omega) (1 - omega^(2)) (1 - omega^(4)) (1 - omega^(5)) (1 - omega^(7)) (1 - omega^(8)) =

Solve: /_\ = |[omega^(3),omega^(4),omega^(5)],[omega^(6),omega^(8),omega^(2)],[omega^(7),omega^(9),omega]|