Question

If $\left|\frac{z-25}{z-1}\right|=5$ , the value of |z|

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (C)

Given that
$\left|\frac{z-25}{z-1}\right|=5\Rightarrow \left|z-25\right|=5\left|z-1\right|$
Let Z = x + iy, then
$\left|x+iy-25\right|=5\left|x+iy-1\right|$
$\Rightarrow \left|\left(x-25\right)+iy\right|=5\left|x-1+iy\right|$
Squaring both sides, we get
${\left(x-25\right)}^2+y^2=25\left\{{\left(x-1\right)}^2+y^2\right\}$
$\Rightarrow x^2-50x+625+y^2$
$=25x^2-50x+25+25y^2$
$\Rightarrow 24x^2+24y^2-600=0$
$\Rightarrow x^2+y^2-25=0$
$\Rightarrow {\left|x+iy\right|}^2=25\Rightarrow {\left|Z\right|}^2=5^2$
$\Rightarrow \left|Z\right|=5$