`omega` is an imaginary root of unity. Prove that `(a+bomega+comega^2)^3+(a+bomega^2+comega^)^3` `=(2a-b-c)(2b-a-c)(2c-a-b)dot`

omega is an imaginary root of unity. Prove that (i) ( a + bomega + comega^(2))^(3) + (a+bomega^(2) + comega)^(3) = (2a-b-c)(2b -a -c)(2c -a-b) (ii) If a+b+c = 0 then prove that (a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc .

If omega be an imaginary cube root of unity, show that (a+bomega+comega^2)/(aomega+bomega^2+c) = omega^2

If a+b+c=0 and omega,omega^2 are imaginary cube roots of unity, then (a+bomega+comega^2)^2+(a+bomega^2+comega)^3= 3abc (b) 6abc (c) 9 abc (d) 27 abc

If a+b+c=0 and omega,omega^2 are imaginary cube roots of unity, then (a+bomega+comega^2)^3+(a+bomega^2+comega)^3= 3abc (b) 6abc (c) 9 abc (d) 27 abc

omega is an imaginary root of unity. Prove that If a+b+c = 0 then prove that (a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc .

If 1, omega and omega^(2) are the cube roots of unity, prove that (a+b omega+c omega^(2))/(c+a omega+b omega^(2))=omega^(2)

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

If |(x^2+x, x-1, x+1), (x, 2x, 3x-1), (4x+1, x-2, x+2)|= px^4 +qx^3+rx^2+sx+t be n identity in x and omega be an imaginary cube root of unity, (a+bomega+comega^2)/(c+aomega+bomega^2)+(a+bomega+comega^2)/(b+comega+aomega^2)= (A) p (B) 2p (C) -2p (D) -p

Let omega be the imaginary cube root of unity and (a+bomega + comega^2)^(2015) =(a+bomega^2 + c omega) where a,b,c are unequal real numbers . Then the value of a^2+b^2+c^2-ab-bc-ca equals.

If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca