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If z is a complex number lying in the fo...

If `z` is a complex number lying in the fourth quadrant of Argand plane and `|[(kz)/(k+1)]+2i|>sqrt(2)` for all real value of`k(k!=-1),` then range of `"arg"(z)` is `(pi/8,0)` b. `(pi/6,0)` c.`(pi/4,0)` d. none of these

A

`(-(pi)/(8),0)`

B

`(-(pi)/(6),0)`

C

`(-(pi)/(4),0)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`kz//(K =1)` represents any point lying on the line joining origin and z.

Given, `|(kz)/(k+1)+2i|gtsqrt(2)`
Hence, `kz//(k+1)` sholud lie outside the circle `|z + 2i| gt sqrt(2)`. So, z shloud lie in the shaded region.
`therefore - (pi)/(4) lt arg(z) lt0`
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