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if z is a complex number belonging to the set `S={z:|z-2+i|gesqrt(5)}` and `z_(0)inS` such that `(1)/(|z_(0)-1|)` is maximum then arg `((4-z_(0)-overline(z)_(0))/(z_(0)-overline(z)_(0)+2i))` is

A

`-pi/2`

B

`pi/4`

C

`pi/2`

D

`(3pi)/4`

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Knowledge Check

  • Let S be the set of all complex numbers z satisfying | -2+i|ge sqrt(5) .if the complex number z_(0) is such that (1)/(|z_0-1|) is the maximum of the set {(1)/(|z-1|): ζinS} , then the principal argument of (4-z_0-overline(z)_0)/(z-overline(z)_0+2i) is

    A
    `(pi)/(4)`
    B
    `(3pi)/(4)`
    C
    `-(pi)/(2)`
    D
    `(pi)/(2)`

  • If z ne 0 be a complex number and "arg"(z)=pi//4 , then

    A
    `"Re"(z)="Im"(z)` only
    B
    `Re(z) = Im(z) gt 0`
    C
    `Re(z^(2))=Im(z^(2))`
    D
    none of these

  • z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0 , then |z| is equal to

    A
    `1/2`
    B
    `3/4`
    C
    1
    D
    none of these

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