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If 1,w,w² are the cube roots of unity then w²(1+w)³-(1+w²)w=? |
| Answer» If 1,w,w² are the cube roots of unity then we have\xa0{tex}{ \\omega }^{ 3 }=1,1+\\omega +{ \\omega }^{ 2 }=0{/tex}w²(1+w)³-(1+w²)w=\xa0{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} | |