Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If z = x + iy such that |z + 1| = |z – 1| and amp 
= 
then
A
x = 
+ 1, y = 0
+ 1, y = 0
B
x = 0, y = 
+ 1
+ 1
C
x = 0, y = 
= 1
= 1
D
x = 
– 1, y = 0
– 1, y = 0
Text Solution
Verified by ExpertsThe correct answer is:
B
|z + 1| = |z – 1| ⇒ (x + 1) 2 + y 2 = (x – 1) 2 + y 2
⇒ x = 0 … (1)
Arg 
= 
⇒ arg 
= 
⇒ arg 
= 
⇒ y > 0, x 2 + y 2 – 1 > 0, 
= 1
⇒ x 2 + y 2 – 2y – 1 = 0, y > 0, x 2 + y 2 – 1 > 0.
∴ arg 
= 
is the arc ABC of the circle x 2 + y 2 – 2y – 1 = 0
Solving with x = 0, we get
y = 
= 1 ± 
, y > 0, ∴ y = 1 + 
.
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