यदी 1, omega, omega^(2) इकाई के घनमूल हो...

यदी `1, omega, omega^(2)` इकाई के घनमूल हो तो सिद्ध कीजिए:
`(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))...."to "2n` गुणनखण्डों तक `=(2)^(2n)`

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

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

Show that (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))...... to 2 n factors =2^(2n)

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

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

(1-omega+omega^2)(1-omega^2+omega^4)(1-omega^4+omega^2)…. to 2n Factors = 2^(2n)

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

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

If 1,omega,omega^(2) are cube roots of unity then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) is equal to