If z=x+i y is a complex number satisfying |z+ i 2 |^2= |z- i 2 |^2 , then the locus of z is

Step-by-step solution

We have, |z+ i 2 |^2= |z- i 2 |^2 array rlrl & |x+i y+ i 2 |^2 & = |x+i y- i 2 |^2 & |x+i (y+ 1 2 ) |^2 & = |x+i (y+ 1 2 ) |^2 & x^2+ (y+ 1 2 )^2 & =x^2+ (y- 1 2 )^2 & x^2+y^2+ 1 4 +y & =x^2+y^2+ 1 4 -y & & 2 y & =0 & y & =0 array Locus of z is x -axis.