The locus of the point z=x+iy satisfying the equation ∣∣∣z−1z+1∣∣∣=1 is given by?
A
x=0
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B
y=0
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C
x=y
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D
x+y=0
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Solution
The correct option is Bx=0 ∣∣z−1z+1∣∣=1 ∴∣∣z−1z+1∣∣=1 ∴|z−1|=|z+1| i.e. lie on the ⊥ bisector the line joining (1,0) & (-1,0) i.e the y axis ∴ 2 lies on x=0.