yeahps, triangle inequality is bauss.
but in this particular question they asked for a locus on argand in part i) so much easier to get it that way imho.
some people dont realise that for med, they don't really have a choice.
u put ur options down- what u get is what u get tbh
and imho, all is good! ( unsw,usyd,uws,...)
the max value is OC + CD from ur locus diagram ( where c is the centre, and D is a point on the external.. radius is 2)
so OC=3ROOT2 AND CD=2 ( radius)
so max l z l = 3root2 +2