Questions & Answers about Я хочу помахать рукой другу.
Both махать and помахать mean “to wave”, but they differ in aspect:
махать – imperfective aspect
- Focuses on a process, repeated or ongoing action.
- Я хочу махать рукой = I want to be (continually) waving my hand / I want to wave repeatedly / for some time.
помахать – perfective aspect
- Focuses on a single, complete action or a short episode of the action.
- Я хочу помахать рукой = I want to wave (once or a little bit), just to do it and be done.
In this sentence, помахать is natural because the speaker wants to wave briefly to someone (e.g. as a greeting or goodbye), not to stand there waving for a long time.