Question

The locus of $z$ such that ${\log }_3|z-1|>{\log }_3|z-i|$ is

• A. $x+y<0$
• B. $x-y>0$
• C. $x+y>0$
• D. $x-y<0$

Answer 1

Answer: (B)

$x-y>0$

$\therefore |z-1|>|z-i|$ $(\because lo{g}_{a}x>lo{g}_{a}y)\Rightarrow x>yifa>1$
$\Rightarrow$ that $z$ is below the line joining points (1,0) and (0,i) i.e $y=xory-x=0$
$\Rightarrow$ for all the points on $z,x>y$

i.e $x-y>0$