`P(z)` be a variable point in the Argand plane such that `|z|=m in i mu m{"|"z-1,|z+1|},t h e nz+ z ` will be equal to a. -1 or 1 b. 1 but not equal to-1 c. -1 but not equal to 1 d. none of these

Options

A. `- 1 or 1`
B. 1 but not equal to `-1`
C. `-1` but not equal to 1
D. none of these

Answer

A

Explanation

When`|z-1|lt|z+1| (or x gt 0)`
`|z|=|z-1|`
`rArr x^(2)+y^(2)=(x-1)^(2)+y^(2)`
`rArr z +barz =1`
When `|z-1|gt|z+1|(or x lt0)`.
`|z|=|z+1|`
`rArr x^(2)+y^(2)=(x+1)^(2)+y^(2)`
`rArr =-1//2`
`rArr z + barz =-1`