Hi,
1. Draw the two circles.
2. To find max arg(z - w), we draw a straight line with a
positive slope in a way that it is tangent to the two circles. Then
use similar triangles and the sine ratio. Look at the diagram I
have drawn here:
http://www.freewebs.com/weews/complexnumbers.htm
3. To find min arg(z - w), we draw a straight line with
a negative slope in a way that it is tangent to the two
circles. Then use similar triangles and the sine ratio.
It is a nice question that is also challenging because
there are two variable points z and w. Cambrige would just ask
arg(z - p) where p is some fixed complex number, e.g. arg(z -
2i).
Thanks!
Cheers,
Wen Shih