Question

Let a, b be two real numbers such that ab < 0. If the complex number \(\frac{1 + ai}{b + i}\) is of unit modulus and a + ib lies on the circle |z – 1| = |2z|, then a possible value of \(\frac{1 + [a]}{4b}\), where [t] is greatest integer function, is :

(1) - 1/2

(2) –1

(3) 1

(4) 1/2

Answer 1

Similarly it is not matching with \(a = \frac{-1- \sqrt 7}6\).