inverse of a point $p$ respect to the circle $|z-z_0 |= r$ in complex

Question

I was solving a problem to find the inverse of a point $p$ respect to the circle $|z-z_0|=r$. In my question I had to find inverse of $1+i$ w.r.t circle $|z+1-2i| = 2$. I applied the formula $q = z_0 + \frac{r^2}{\overline{p} - \overline{z_0}}$ where q is inverse of point $p$. By this i got $q = -1+2i + \frac{4}{1-i-(-1-2i)}$. But I am getting the wrong answer. Please help. Where I did wrong. Kindly give suggestions . thanks

Answer 1

The last term $\frac{4}{2+i}$ is $\frac{8-4i}{5}$. (I multiplied top and bottom by $2-i$.)

When we add $-1+2i$ we get $\frac{3+6i}{5}$. For $-1+2i=\frac{-5+10i}{5}$.