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

Options

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

Answer

C

Explanation

`|z-(2-i)|gesqrt(5)`
for `|z_(0)-1|` to be minimum `z_(0)=x_(0)+iy_(0)` is at point P as shown in figure
`arg(4-(z_(0)+overline(z)_(0))/(z_(0)-overline(z)_(0)+2i))=arg((4-2x)/(2iy+2i))=arg((-i(2-x))/(y+2))=arg(-ilamda)=-(pi)/(2)" "(becauselamda gt 0)`