Given equation is: |z + 1| = |z – 1| Let the value of ‘z’ be: z = x + iy Now, the equation becomes, ⇒ |(x + iy) + 1| = |(x + iy)-1| ⇒ |(x + 1) + iy| = |(x – 1) + iy| On taking modulus on both sides, ⇒√(x+1)2+y2=√(x−1)2+y2 ⇒√x2+2x+1+y2=√x2−2x+1+y2 On squaring on both sides, we get ⇒x2+2x+1+y2=x2−2x+1+y2 ⇒4x=0 ∴x=0 Therefore, the equation represents y-axis.