1. The problem statement, all variables and given/known data This is a CIE A'level maths P3 question out of an exam from 2013 in October/November. As there is no markscheme ( I at least can't find one), I would be grateful if someone could look at my solution to the problem and correct me if I made a mistake. The problem is 8.(b) below. 2. Relevant equations 3. The attempt at a solution The first locus they are asking for is that of a circle with centre (0,-1) and radius 1 and the second locus is a line 135 deg. to the horizontal (real number axis) starting at x=2. I call z1 and z2 the points which will give the least value of abs(z-w). Both these points must lie on a line l2. My further working and sketch of loci and the line are in the following image.In the last step I use the distance formula for the two complex numbers I calculated in the earlier steps. In the earlier steps I equated the equation of l2 and the equations for the loci. Thanks for any effort! And sorry for the clumsy exposition!