JEE Mains Model Paper 9

Let z = x + iy
⏐z − 1⏐ = ⏐z + 1⏐ ⇒ Re z = 0 ⇒ x = 0
⏐z − 1⏐= ⏐z − i⏐ ⇒ x = y
⏐z + 1⏐= ⏐z − i⏐ ⇒ y = −x
Only (0, 0) will satisfy all conditions.
⇒ Number of complex number z = 1