`(a+b)(aomega^4+bomega^8)(aomega^2+bomega^7)`

If omega ne 1 is a cube root of unity and a+b=21 , a^(3)+b^(3)=105 , then the value of (aomega^(2)+bomega)(aomega+bomega^(2)) is be equal to

If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+aomega+bomega^2)=omega^2

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

The value of (a+bomega+comega^2)/(b+comega+aomega^2)+(a+bomega+comega^2)/(c+aomega+bomega^2) (where 'omega' is the imaginary cube root of unity), is a.-omega b. omega^2 c. 1 d. -1

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

Statement-1: If a,b,c are distinct real number and omega( ne 1) is a cube root of unity, then |(a+bomega+comega^(2))/(aomega^(2)+b+comega)|=1 Statement-2: For any non-zero complex number z,|z / bar z)|=1