In a manner characterized by smug self-satisfaction or complacence; with an oblivious and self-contented attitude.
From complacential + -ly (adverbial suffix). The -ly suffix converts adjectives to adverbs. This is an extremely rare formation, as 'complacently' is vastly more common.
The word 'complacentially' is so rare that most spell-checkers flag it as incorrect, preferring 'complacently'—it's a perfect example of how speakers eliminate redundant long forms in favor of simpler alternatives. Creating adverbs from adjectives is so automatic in English that people invent forms like this without realizing simpler versions already exist.
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