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Statement-1: If a,b,c are distinct real ...

Statement-1: If a,b,c are distinct real number and `omega( ne 1)` is a cube root of unity, then `|(a+bomega+comega^(2))/(aomega^(2)+b+comega)|=1`
Statement-2: For any non-zero complex number `z,|z/barz|=1

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Knowledge Check

  • Statement-1: If a,b,c are distinct real number and omega( ne 1) is a cube root of unity, then |(a+bomega+comega^(2))/(aomega^(2)+b+comega)|=1 Statement-2: For any non-zero complex number z,|z / bar z)|=1

    A
    Statement-1 is True, Statement-2 is True: Statement-2 is a correct exp,anation for statement-1.
    B
    Statement-1 is true, statement -2 is true, Statement-2 is not a correct explanation for statement-1.
    C
    Statement-1 is True, statement-2 is false,
    D
    statement-1 is False, Statement-2 is true.

  • If omega ne 1 is a cube root of unity, then 1, omega, omega^(2)

    A
    are vertices of an equilateral triangle
    B
    lie on a straight line
    C
    lie on a circle of radius `sqrt(3//2)`
    D
    None of these

  • 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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