Sketch the locus of thepoint representing complex number z such that |z - 2 - 2i| =1
Sketch the locus of the point representing complex number w such that |w + 4 - 2i| =2
Hence find the max and min values of arg(z-w)
Thanks in advance for your help
the ans given is pi/6 and -pi/6
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
oh ok .. wow sounds complicated. thanks for ur help
http://docs.google.com/present/view?id=dfzsf6p3_102cgmqrr74
i drew a simple diagram... maybe u can help me see whether i did it right?
where is the angle that we are interested in ?
oops i just saw the diagram you have drawn ..thanks