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.

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