root 1+ a2+ root 1 + a2+ a4=
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Since, 1,a1,a2,....,an−1 are the nth root of unity.
Since, 1,a1,a2,....,an−1 are the nth root of unity.∴xn−1=(x−1)(x−a1)...(x−an−1)
Since, 1,a1,a2,....,an−1 are the nth root of unity.∴xn−1=(x−1)(x−a1)...(x−an−1)⇒x−1xn−1=(x−a1)(x−a2)....(x−an−1)
Since, 1,a1,a2,....,an−1 are the nth root of unity.∴xn−1=(x−1)(x−a1)...(x−an−1)⇒x−1xn−1=(x−a1)(x−a2)....(x−an−1)∴xn−1+xn−2+...+x2+x+1
Since, 1,a1,a2,....,an−1 are the nth root of unity.∴xn−1=(x−1)(x−a1)...(x−an−1)⇒x−1xn−1=(x−a1)(x−a2)....(x−an−1)∴xn−1+xn−2+...+x2+x+1=(x−a1)(x−a2)....(x−an−1)
Since, 1,a1,a2,....,an−1 are the nth root of unity.∴xn−1=(x−1)(x−a1)...(x−an−1)⇒x−1xn−1=(x−a1)(x−a2)....(x−an−1)∴xn−1+xn−2+...+x2+x+1=(x−a1)(x−a2)....(x−an−1)Put x=1, we get
Since, 1,a1,a2,....,an−1 are the nth root of unity.∴xn−1=(x−1)(x−a1)...(x−an−1)⇒x−1xn−1=(x−a1)(x−a2)....(x−an−1)∴xn−1+xn−2+...+x2+x+1=(x−a1)(x−a2)....(x−an−1)Put x=1, we get(1−a1)(1−a2)...(1−an−t)=1+1+...+n times
Since, 1,a1,a2,....,an−1 are the nth root of unity.∴xn−1=(x−1)(x−a1)...(x−an−1)⇒x−1xn−1=(x−a1)(x−a2)....(x−an−1)∴xn−1+xn−2+...+x2+x+1=(x−a1)(x−a2)....(x−an−1)Put x=1, we get(1−a1)(1−a2)...(1−an−t)=1+1+...+n times=n.
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