Let a, b be two real numbers such that a b<0. If the complex number (1+a i)/(b+i) is of unit modulus and a +i b lies on the circle |z-1|=|2 z|, then…

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