Q49 / 90 · JEE Main 2010 · Mathematics

The number of complex numbers $z$ such that $|z-1|=|z+1|=|z-i|$ equals

  • Correct answer
    A
    1
  • B
    2
  • C
    $\infty$
  • D
    0

Solution

Let $z=x+i y$ $$ \begin{array}{lll} |z-1|=|z+1| & \Rightarrow \operatorname{Re} z=0 & \Rightarrow x=0 \\ |z-1|=|z-i| & \Rightarrow x=y & \\ |z+1|=|z-i| & \Rightarrow y=-x & \end{array} $$ Only $(0,0)$ will satisfy all conditions. $\Rightarrow$ Number of complex number $z=1$

Hence, the correct answer is option: 'A'.

Relevant Questions