> 
> Sketch, on a single Argand diagram, the loci given by
> 
> 
> (i) $| z − \sqrt 3 − i | = 2$
> 
> 
> (ii) $\arg (z) = 16 \pi$
> 
> 
> 

Does anyone know a good way of how to explain solving a problem similar or the same as this?

The part $| z − \sqrt3 − i | = 2$ is just a circle at $(\sqrt3,1)$ that crosses the point $(0,0)$ [why?] and is its radius $\sqrt2$?

Second part I don't understand at all.