If 1,w,w² are the cube roots …
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Posted by Aman Kumar 8 years, 5 months ago
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Rasmi Rv 8 years, 5 months ago
If 1,w,w² are the cube roots of unity then we have {tex}{ \omega }^{ 3 }=1,1+\omega +{ \omega }^{ 2 }=0{/tex}
w²(1+w)³-(1+w²)w= {tex}{ \omega }^{ 2 }{ \left( -{ \omega }^{ 2 } \right) }^{ 3 }-\left( -\omega \right) .\omega ={ \omega }^{ 2 }.{ -\omega }^{ 6 }+{ \omega }^{ 2 }=-{ \omega }^{ 8 }+{ \omega }^{ 2 }=-{ \omega }^{ 3 }.{ \omega }^{ 3 }.{ \omega }^{ 2 }+{ \omega }^{ 2 }=-{ \omega }^{ 2 }+{ \omega }^{ 2 }=0{/tex} {tex}\\ \left[ \because { \left( { a }^{ m } \right) }^{ n }={ a }^{ mn },{ a }^{ m }.{ a }^{ n }={ a }^{ m+n } \right] {/tex}
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