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If z=-1, the principal value of arg. (z^...

If `z=-1`, the principal value of arg. `(z^(2//3))` is equal to :

A

`(pi)/(3)`

B

`(2pi)/(3)` or `2pi`

C

`(10pi)/(3)`

D

`pi`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The value of (z+3)(bar(z)+3) is equivalent to

    A
    `|z+3|^(2)`
    B
    `|z-3|`
    C
    `z^(2)+3`
    D
    none of these

  • If x, y, z are all different and not equal to zero and |{:(1+x,,1,,1),(1,,1+y,,1),(1,,1,,1+z):}| = 0 then the value of x^(-1) + y^(-1) + z^(-1) is equal to

    A
    xyz
    B
    `x^(-1)y^(-1)z^(-1)`
    C
    `-x-y-z`
    D
    `-1`

  • Let z_(1) and z_(2) be two distinct complex numbers and let z=(1-t)z_(1)+tz_(2) for some real number t with 0 lt t lt 1 . If Arg (w) denotes the principal argument of a non zero complex number w , then

    A
    `|z-z_(1)|+|z-z_(2)|=|z_(1)-z_(2)|`
    B
    Arg`|z-z_(1)|=Arg|z-z_(2)|`
    C
    `|{:(z-z_(1),barz-barz_(1)),(z_(2)-z_(1),barz_(2)-barz_(1)):}|=0`
    D
    `Arg(z-z_(1))=Arg(z_(2)-z_(1))`

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