Q45 of 66 Page 91

The complex number z which satisfies the condition lies on

Given


Let z = x + yi




⇒ |x + (y + 1) i| = |-x – (y – 1) i|



⇒ x2 + (y + 1)2 = x2 + (y – 1)2


⇒ (y + 1)2 = (y – 1)2


⇒ y2 + 2y + 1 = y2 – 2y + 1


⇒ 2y = -2y


⇒ 4y = 0


⇒ y = 0 (x – axis)

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