Movement of $1/z$ in complex plane How is moving $\frac{1}{z}$ in complex plane if $z$ is described by a circle which has radius $r$ and center $a+b*i$
I've just started complex algebra and still having some trouble imagining it.
How one does even solve this kind of problems, I don't want the complete solution I just want some appropriate ways for working with complex numbers to solve this kind of problems. 
Thank you.)

Hint: Compute $\dfrac1{r\bigl(\cos(\theta)+i\sin(\theta)\bigr)}$.
