What is minimum value of |a+bw+cw^2|? whrere w is cube root of unity?

[vkash]

a,b,c are integers not all equal and w is the cube root of unity then minimum value of |a+bw+cw²|(w is not equals one).

My answer
|a+bw+cw²|<=|a|+|bw|+|cw²|
|a|+|bw|+|cw²|=a+b+c.
so at lest one value of |a+bw+cw²| will smaller than the minimum value of a+b+c. for integers this minimum value is smallest integers you can think of.
But that's wrong.?why?

 

[Simon Bridge]

Is |w²| = 1?