Q10 of 66 Page 91

Show that the complex number z, satisfying the condition arg lies on a circle.

Let z = x + iy


Given


⇒ arg (z – 1) – arg (z + 1) = π/4


⇒ arg (x + iy – 1) – arg (x + iy + 1) = π/4


⇒ arg (x – 1 + iy) – arg (x + 1 + iy) = π/4






⇒ x2 + y2 – 1 = 2y


⇒ x2 + y2 – 2y – 1 = 0


Which represents a circle.


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