IPA: /kəmˈpleɪnɪŋli/
KK: /kəmˈpleɪnɪŋli/
In a way that shows dissatisfaction or annoyance about something.
She spoke complainingly about the long wait at the restaurant.
Complainingly → It is formed from "complain" (from Old French *compleindre*, meaning to express dissatisfaction) and "-ingly" (a suffix used to form adverbs indicating manner). The word "complainingly" means in a manner that expresses dissatisfaction or annoyance.
Think of expressing dissatisfaction ('complain') in a certain manner ('-ingly') — that's what complainingly means.