Complex is the opposite of simple. Complicated is the opposite of easy.

A simple road, for instance, has only one lane and goes only in one direction. A complex road may have only one lane but may branch out into many directions and some of the branches may intersect with each other. However, a simple idea may be infinitely more difficult to understand and/or express than a complex one. A maze has a complex path. It is fairly easy to draw a maze. But try explaining "zero".

Complicated means that you need to take into account several different factors. Say you want to build a house. But the ground is sloping. You can build your house to match the slope, in which case you will need to nail down everything in the house so things don't keep sliding all the time. Or you can build against the slope. But then one side of the house will be higher than the other. There is a solution. But it is complicated.