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Question:

That ω≠1 be a cube root of unity. Then the minimum of the set |a+bω+cω²|²; a, b, c are distinct non-zero integers equals _________.

3.00

Solution:

Correct option is A. 3.00
|a+bω+cω²|²=a²+b²+c²-ab-bc-ca=1/2[(a-b)²+(b-c)²+(c-a)²]
It will be minimum when a, b, c are consecutive integers so minimum value is 3.