if `|(z-6)/(z+8)|=1`, then the value of `x in R`, where `z=x+i|{:(-3,2i,2+i),(-2i,2,4-3i),(2-i,4+3i,7):}|`, is

Options

A. 5
B. 7
C. 9
D. 0

Answer

B

Explanation

We have,
`|(z-6)/(z-8)|=1`
`rArr |z-6|=|z-8|`
`rArr` z lies on the perpendicular bisector of the segment joining (6,0) and (8,0), i.e., `x=7`.
`rArr x=7+iy`, where `y in R`…………….(i)
Now,
`z=x+i|{:(-3,2i,2+i),(-2i,2,4-i),(2-I,4+3i,7):}|=x+35i` .................(ii)
From (i) and (ii), we get `x=7`.