Let C be the circle in the complex plane with centre z_0=1/2(1+3 i) and radius r=1. Let z_1=1+ i and the complex number z_2 be outside the circle C…

Let $\displaystyle C$ be the circle in the complex plane with centre $\displaystyle \mathrm{z}_0=\frac{1}{2}(1+3 i)$ and radius $\displaystyle r=1$. Let $\displaystyle \mathrm{z}_1=1+\mathrm{i}$ and the complex number $\displaystyle z_2$ be outside the circle $\displaystyle C$ such that $\displaystyle \left|z_1-z_0\right|\left|z_2-z_0\right|=1$. If $\displaystyle z_0, z_1$ and $\displaystyle z_2$ are collinear, then the smaller value of $\displaystyle \left|z_2\right|^2$ is equal to