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The minimum value of |alpha bomega+comega^2| , where a, b and c are all not equal integer and omega( ne 1) is a cube root of unity , is |
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Answer» `sqrt(3)` `rArrz^2 = |alpha + b omega+ comega^2|=(a^2 + b^2 +c^2-ab-bc -ca)or z^2=1/2{(a-b)^2+(b-c)^2+(c-b)^2}` since a,b,care all intergers but not all simulataneously EQUAL `RARR ` If a=bthen `a ne c and be ne c ` Because DIFFERENCE of intergerse = interger ` rArr(b-c)^2 le 1 ` and we have taken `a= b rArr (a -b)^2 =0` From EQ.(i)`z^2ge 1/2 (0+1+1)` `rArr z^2ge 1` Hence minimum value of |Z| is 1 |
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