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`a ,b , c` are integers, not all simultaneously equal, and `omega` is cube root of unity `(omega!=1)` , then minimum value of `|a+bomega+comega^2|` is `0` b. `1` c. `(sqrt(3))/2` d. `1/2`

A

`sqrt(3)`

B

1

C

2

D

3

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • . If a b, and c are integers not all equal and omega is a cube root of unity (where omega ne 1 ), then minimum value of |a + b omega + c omega ^(2)| ^(2) is equal to

    A
    0
    B
    1
    C
    `(sqrt3)/(2)`
    D
    `(1)/(2)`

  • If a, b, c are integers not all equal and w is a cube root of unity (w ne 1) , then the minimum value of |a+ bw+ cw^2| is

    A
    `0`
    B
    `1`
    C
    `1//2 lt |z| lt 3//4`
    D
    `1//2`

  • If a,b,c are distinct integers and omega(ne 1) is a cube root of unity, then the minimum value of |a+bomega+comega^(2)|+|a+bomega^(2)+comega| is

    A
    `2sqrt(3)`
    B
    3
    C
    `4sqrt(2)`
    D
    2

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