Complex loci problem
I know this locus is a circle, but only because I recognise the form, I cannot see how to show it algebraically.
I would like to find the centre and radius (or its equation).
The second part of the question asks to show that is constant on this circle, but I don't even know what it's asking for that one!
Any nudges in the correct direction would be great, not asking for a full solution, just some help getting started.
Thanks! I did a bit of hunting around the web and found a method which involved taking the tangent of both sides and then using the identity for tan(A-B), I will try both methods and see if I get the same equation for the circle.
When going the tangent route, can the additional condition be obtained by noting that if has an argument of then it must be in the second quadrant, so it's real part negative and imaginary part positive?
Yes, that's exactly the reason.
Originally Posted by Stonehambey