A point $z$  moves on Argand diagram in such a way that $\left|z-3i\right|=2$ , then its locus will be:

$\left|z-3i\right|=2,$  let  $z=x+iy\Rightarrow \left|x+i\left(y-3\right)\right|=2$

Squaring both sides, we get $\left[x^2+{\left(y-3\right)}^2\right]=4$

$\Rightarrow$           $x^2+y^2-6y+5=0$ .