Complacent means self-satisfied, smug, or contented to a fault. Complaisant, a relatively recent loanword from French, means cheerfully obliging or tending to go along with others.
Both have negative connotations when applied to a person, and they might share a little common ground, but they’re easy to keep separate. Think of a complacent person as someone who is willfully ignorant, unconcerned, or overcontented, while a complaisant person is a pushover, willing to do whatever anyone asks.
Given the nonmanufacturing index is seen as a good leading indicator of growth, investors shouldn’t grow complacent. [Wall Street Journal]
It’s generally considered today that Pasok, which continues to dominate the interim coalition, has all along been complaisant and compliant towards EU impositions. [Irish Times]
Henry Miller set out to shock the complacent American bourgeoisie with his heady mix of sex and philosophy. [Guardian]
[Their] emotional ménage à trois is more potent than the one Jung is having with Sabina and his complaisant wife. [Guardian]
The ruling British lived a complacent, comfortable life, overseeing the activities of the Malay, Chinese, Arab and Indian residents. [The Australian]
But my goat, Cookie, was complaisant and calm. [Chron]