Math Help Forum - View Single Post - 1 sum. elementary transformation from z-plane to w-plane (complex number)

ssadi · #1 December 3rd, 2008, 05:58 AM

For the transformation $w=z^2$ 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, $|w|=4$ , but how do show that it moves twice?

2. If i take $|z|=2, w=z^2, z=\sqrt w, |z|=|\sqrt w|=2$ : how do I do this part: $2=|\sqrt w|$ , when w is a complex number?
And how do i carry out from there :help: