FP2 Complex Number Loci

Paper (I hope the link works...)
http://crashmaths.com/wp-content/uploads/2017/03/FP2PPBQP.pdf
Mark Scheme:
https://crashmaths.com/wp-content/uploads/2017/03/FP2PPBMS.pdf

I was working through the CrashMATHS FP2 practice paper B noticed that the domain for the Cartesian equation for question 5 was x<0, and not x is less than or equal to zero. Could someone explain to my why this is? I think I have seen something similar before but I'm not sure. Also, can anyone provide a better description of the curve in question 6a than 'arc'...? I'm not sure if what I described was right... I thought since sintheta + costheta is, if I'm correct, the same as root2 times sin(theta + pi/4), that it would be like the graph for root 2 times sintheta but rotated by pi/4 anticlockwise? Or something similar? I guess that would be an arc in the given range so perhaps that is right?


Thank you for any help!

Q5: At e.g. (0,-2), i.e. z=-2i, the argument becomes arg(-6i/0), and as division by zero is undefined, we can't have this, so we must exclude the boundary points at which x=0.

Q6a: There isn't really a better description than "arc". Your idea about the rotation is almost right, but it would be a rotation by pi/4 clockwise, just as y=f(x+3) is a translation of f(x) not 3 units to the right, but 3 units to the left.