1 sum. elementary transformation from z-plane to w-plane (complex number)

For the transformation $\displaystyle w=z^2$ show that as z moves once round the circle centre O and radius 2, w moves twice round the circle center O and radius 4.

I have two problems for which I am stuck on the sum:

1. How do moving "once" and "twice" is represented on the equation? That is, if w lies on circle center O and radius 4, $\displaystyle |w|=4 $, but how do show that it moves **twice**?

2. If i take $\displaystyle |z|=2, w=z^2, z=\sqrt w, |z|=|\sqrt w|=2$: how do I do this part: $\displaystyle 2=|\sqrt w|$, when w is a complex number?

And how do i carry out from there :help: