What `omegane1` be a cube root of unity. Then minimum value of set `{|a+bomega+comega^(2)|^(2)`, a,b,c are distinct non zero intergers) equals

Answer

3

Explanation

`|a+bomega+comega^(2)|^(2)=a^(2)+b^(2)+c^(2)-ab-bc-ca=(1)/(2){(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}`
it will be minimum when `a=1,b=2,c=3`
so minimum value is 3.