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

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MINIMUM value of | a+bw+cw^2| when a b c are distinct integers and w is cube root of unity not1MINIMUM value of | a+bw+cw^2| when a b c are distinct integers and w is cube root of unity not1
1.e) (a+bω+cω²)/(aω+bω²+c) + (a+bω+cω²)/(aω²+b+cω) = –1 If ω be complex cube root unity show that :1.e) (a+bω+cω²)/(aω+bω²+c) + (a+bω+cω²)/(aω²+b+cω) = –1 If ω be complex cube root unity show that :
if w is cube root of unity then find the value of (a+bw+cw^2)/(c+aw+bw^2).if w is cube root of unity then find the value of (a+bw+cw^2)/(c+aw+bw^2).
a3 + b3 + c3 - 3abc = ? (A Cube+ B Cube + C Cube- 3abc ) Formula of a cube plus b cube plus c cubea3 + b3 + c3 - 3abc = ? (A Cube+ B Cube + C Cube- 3abc ) Formula of a cube plus b cube plus c cube
If `a , b , c` are real numbers, prove that `|a b c b c a c a b|=-(a+b+c)(c+b w+c w^2)(a+b w^2+c...If `a , b , c` are real numbers, prove that `|a b c b c a c a b|=-(a+b+c)(c+b w+c w^2)(a+b w^2+c...
a+bw+cw^2/b+cw+aw^2=wa+bw+cw^2/b+cw+aw^2=w
The value of (a+bω+cω^2)/(c+aω+bω^2 ) where ω is a complex cube root of unity, isThe value of (a+bω+cω^2)/(c+aω+bω^2 ) where ω is a complex cube root of unity, is
Compute (a+bw+c*w^2)(a+b*w^2+cw) where w = -1/2 + i*sqrt(3)/2.Compute (a+bw+c*w^2)(a+b*w^2+cw) where w = -1/2 + i*sqrt(3)/2.