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z= -1-isqrt(3)...

` z= -1-isqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
`-(2pi)/(3)`.
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Explore conceptually related problems

If the complex number z_1,z_2 and z_3 represent the vertices of an equilateral triangle inscribed in the circle |z|=2 and z_1=1+isqrt(3) then (A) z_2=1,z_3=1-isqrt(3) (B) z_2=1-isqrt(3),z_3=-isqrt(3) (C) z_2=1-isqrt(3), z_3=-1+isqrt(3) (D) z_2=,z_3=1-isqrt(3)

Find the pricipal argument of each of the following: (a) -1-isqrt(3) (b) (1+sqrt(3)i)/(3 +i) (c) sin alpha + i(1-cos alpha), 0 gt alpha gt pi (d) (1+ isqrt(3))^(2)

Knowledge Check

  • Find the argument of -1 -isqrt(3)

    A
    `2`
    B
    `(-2pi)/(3)`
    C
    `(5pi)/(6)`
    D
    None of these

  • The modulus of the complex number z= ((1-isqrt3)(costheta+isintheta))/(2(1-i)(costheta-isintheta)) is

    A
    `1/sqrt2`
    B
    `1/(2sqrt2)`
    C
    `1/sqrt3`
    D
    None of these

  • What is the value of : ((-1+isqrt(3))/(2))^(3n) + (( -1-isqrt(3))/(2))^(3n) Where, i= sqrt( -1) ?

    A
    3
    B
    2
    C
    1
    D
    1

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    Supose z_(1),z_(2),z_(3) are vertices of an equilateral triangle in an argand plane inscribed in the circle |z|=2 . If z_(1)=1-isqrt(3),z_(2)=a+ib,z_(3)=c+id , wher a,b,c in R and a gtc , then |3a+d-c| to

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    The argument of ((1-isqrt(3)))/((1+isqrt(3))) is

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