Complex or Complicated?

Copy editors, including me, can really get into the weeds. Today, I am thinking about complex versus complicated.

We generally use complex to mean a whole made up of lots of parts. Machines are complex.

We generally use complicated to mean involved. Relationships are complicated.

Except that complicated can also mean parts making up a whole. Machines can, in fact, be complicated or complex.

But—and here's where it gets tricky—relationships can't be complex. (Well, maybe a ménage à trois could be?)