If `|(z-25)/(z-1)| = 5 ` , the value of `|z|` is -

Options

A. 3
B. 4
C. 5
D. 6

Answer

C

Explanation

Let `z=x+iy`
`therefore" "|(z-25)/(z-1)|=5" "rArr" "|((x-25)+iy)/((x-1)+iy)|=5" "rArr" "|(x-25)+iy|=5|(x-1)+iy|`
`rArr" "sqrt((x-25)^(2)+y^(2))=5sqrt((x-1)^(2)+y^(2))`
On squaring both sides, we get
`(x-25)^(2)+y^(2)=25{(x-1)^(2)+y^(2)}" "rArr" "x^(2)-50x+625+y^(2)=25x^(2)-50x+25+25y^(2)`
`rArr" "24x^(2)+24y^(2)=600" "rArr" "x^(2)+y^(2)=25`
`rArr" "sqrt(x^(2)+y^(2))=5" "[because |z|=sqrt((x^(2)+y^(2)))]" "rArr" "|z|=5`