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

  1. Nov 20, 2011 #1
    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???
     
  2. jcsd
  3. Nov 21, 2011 #2

    Simon Bridge

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    Is |w2| = 1?
     
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