1.

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

Answer»

`sqrt(3)`
`1/2`
1
0

Solution :Let`Z|alpha+bomega +comega^2|`
`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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