`(a+b)+(aw+bw^2)+(aw^2+bw)=0`

(a+b) (a omega+b omega^(2)) (aw^(2)+bw) =?

prove: (a+b+c)(a+bw+cw^(2))(a+bw^(2)+cw)=a^(3)+b^(3)+c^(3)-3abcw is cube root of unity

If x=a+b,y=aw+bw^(2) and z=aw^(2)+bw, where w is an imaginary cube. root of unity,prove that x^(2)+y^(2)+z^(2)=6ab

How many terms are there in the expansion of ((a^2)/(b^2) + (b^2)/(a^2) + 2)^21 where a a != 0,b != 0?

If a!=b!=c\ a n d\ |{:(a, b, c), (a^2,b^2,c^2), (b+c, c+a, a+b):}|=0 then a+b+c=0 b. a b+b c+c a=0 c. a^2+b^2+c^2=a b+b c+c a d. a b c=0

If a+b+c=0 , find the value of (a^2)/((a^2-b c))+(b^2)/((b^2-c a))+(c^2)/((c^2-a b)) (a) 0 (b) 1 (c) 2 (d) 4

The points (-a, -b), (0, 0),(a, b) and (a^(2),ab) are

If sum_(k=0)^(n)(a+bw^(k))(b+cw^(k))(c+aw^(k)) is purely a real number,when a,b,care distinct real numbers and w is a complex root of unity, then which of the following cannot be the value of n: