The locus of the point z=x+iy satisfying the equation (z-1)(z+1)=1 is given by
x=0
y=0
x=y
x+y=0
Explanation of the correct option.
Compute the locus:
Given: (z-1)(z+1)=1
⇒ (z-1)=(z+i)
Take z=x+iy
⇒ x+iy-1=x+iy+1
⇒ x-12+(y)2=(x+1)2+(y)2
⇒ x2+1-2x+y2=x2+1+2x+y2
⇒ 4x=0
⇒ x=0
Hence the locus of the point is x=0.
Option A is the correct answer.