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lf z1,z2,z3 are vertices of an equilater...

lf `z_1,z_2,z_3` are vertices of an equilateral triangle inscribed in the circle `|z| = 2` and if `z_1 = 1 + iotasqrt3` , then

Text Solution

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The correct Answer is:
`z_(2) = - 2 , z_(3) = 1 -isqrt(3)`
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Knowledge Check

  • If z_1, z_2, z_3 are the vertices of an equilateral triangle inscribed in the circle |z|=1 then the area of the triangle having z_1 , z_2, z_3 as its vertices is

    A
    `(sqrt3)/(2)`
    B
    `(sqrt3)/(4)`
    C
    `( 3 sqrt3)/(4)`
    D
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  • If z_(1),z_(2),z_(3) be vertices of an equilateral triangle occurig in the anticlockwise sense, then

    A
    `z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=2(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))`
    B
    `1/(z_(1)+z_(2))+1/(z_(2)+z_(3))+1/(z_(3)+z_(1))=0`
    C
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    D
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  • If z _(1) , z _(2) and z _(3) represent the vertices of an equilateral triangle such that

    A
    `z _(1) + z _(2) = z _(3)`
    B
    `z _(1) + z _(2) + z _(3) =0`
    C
    `z _(1) z _(2) = (1)/( z _(3))`
    D
    `z _(1) - z _(2) = z _(3) - z _(2)`

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