Question

The complex number z which satisfies the condition |i + z/i - z| = 1 lies on

A. circle x² + y² = 1
B. the x-axis
C. the y-axis
D. the line x + y = 1

Answer 1

B. the x-axis

⇒ 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)