Hello Mav
Let's say you're an Inland Revenue helpdesk official in the GLASGOW office.
MrP calls you with a relatively simple query. Usually, of course, an Inland Revenue helpdesk official in the GLASGOW office will make the answer as absurd, inconsistent, and downright incomprehensible as possible. That's his job, after all. He's on a 'helpdesk', after all, isn't he? (In the GLASGOW office.)
But not you. You are willing to help MrP. You agree to everything he suggests, even though he is quite rude at first and shouts once or twice. You answer his question in simple, effective English. His interpretation of 'legitimate expenses' is wholly correct. You suggest other useful deductions that MrP might make. You even propose a full rebate. MrP begins to weep.
In short, you are 'complaisant'. Later, at home, you think back on your day. You feel particularly pleased about the way you handled MrP. You look in the mirror and say to yourself, you did pretty well there, Mav. In short, you are complacent about your complaisance.
Now the antonym would mean "unwilling to please others or to accept their behaviour without protest". So in this instance, you couldn't really say that "this complacence was still a result of the antonym of complaisance".
MrP
PS Did I mention the location of the tax office? It was in GLASGOW, if anybody's wondering.