www.alphadictionary.com

This can be either an adjective or a noun. To quote Tom Lehrer, "You may end up with a quite complex complex."

The opposite of simple, complex as a noun can refer to a unified group of buildings (a hospital complex) or a medical or psychiatric diagnosis, and possibly other collections of related things.

Related to complicit. Accomplice, too, but not accomplish.

And presumably related to complexion? Goodness knows how we get from peaches-and-cream to psychological disturbance.

From etymonline:

The specific meaning "color or hue of the skin of the face" developed by mid-15c. In medieval physiology, the color of the face was believed to indicate temperament or health.