1. in a manner showing a desire to please or oblige; obligingly
Usage: formal; often implies excessive eagerness to please
2. in a self-satisfied or smug manner
Usage: often carries a negative connotation

Examples

• She complaisantly agreed to all his requests without question.
• He smiled complaisantly, clearly pleased with his own performance.
• The host complaisantly accommodated every guest's dietary preference.
• She nodded complaisantly, as if she had always known the answer.
• He accepted the praise complaisantly, showing little humility.
• The servant complaisantly attended to every need of the household.