Let z ∈ C be such that z < 1 . If ω = 5 + 3 z 5 1 - z , then:

Step-by-step solution

Given z < 1 and ω = 5 + 3 z 5 1 - z ⇒ 5 ω 1 - z = 5 + 3 z ⇒ 5 ω - 5 ω z = 5 + 3 z ⇒ z = 5 ω - 5 3 + 5 ω Using the given condition z = 5 ω - 1 3 + 5 ω < 1 ⇒ 5 ω - 1 < 3 + 5 ω ⇒ 5 ω - 1 < 5 ω + 3 5 ⇒ ω - 1 < ω - - 3 5 We know that the locus of a complex number z 1 satisfying z 1 - a = z 2 - b is the perpendicular bisector of the line segment joining the points a and b . Hence, the locus of the