Question

यदि `1,omega` तथा `omega^(2)` इकाई के घनमूल है तो सिद्ध कीजिए कि -
(i) `omega(1+omega-omega^(2))=-2`
(ii) `(1+omega-omega^(2))(omega+omega^(2)-1)(omega^(2)+1-omega)=-8`
(iii) `omega^(4)+2omega^(6)+omega^(8)=1`
(iv) `(3+3omega+5omega^(2))^(6)-(2+6omega+2omega^(2))^(3)=0`
(v) `(1+omega)(1+omega^(2))(1+omega^(4))(1+omega^(8))=1`

Answer 1

(ii) बायाँ पक्ष `=(1+omega-omega^(2))(omega+omega^(2)-1)(omega^(2)+1-omega)`
`=(-omega^(2)-omega^(2))(-1-1)(-omega-omega)`
`=(-2omega^(2))(-2)(-2omega)`
`=(-8)omega^(3)=(-8)(1)=-8=` दायाँ पक्ष