The locus of the point z = x + iy satisfying the equation |(z-1)/(z+1)| = 1 is given by (1) x = 0 (2) y = 0 (3) x = y (4) x + y = 0

Solution:

Given |(z-1)/(z+1)| = 1

z = x+iy

Put z in given equation

|x+iy-1)/(x+iy+1)| = 1

√((x-1)²+y²) = √((x+1)²+y²)

Squaring both sides

(x-1)²+y² = (x+1)²+y²

(x+1)²-(x-1)² = 0

4x = 0

x = 0

Hence option (1) is the answer.