I'm writing this letter in purpose of complaining about your after-sale service.

我写这封信要投诉你们的售后服务。

youdao

I was very concerned when I received your letter of yesterday complaining that the central heating system in your new house had not been completed by the date promised.

昨天收到你的来信，抱怨你新家的中央加热系统未按规定时间装好，对此我非常关心。

youdao

The California Highway Patrol issued an alert Thursday morning urging officers in several Southern California counties to be on the lookout for the onetime officer and Navy lieutenant who allegedly threatened police officers and their families in a lengthy letter complaining of his treatment by the Los Angeles Police Department.

CNN: California police look for ex-cop suspected in shootings

Dorner blamed the retired officer for bungling his appeal to get his job back, according to a letter he wrote complaining of mistreatment by the LAPD.

CNN: STORY HIGHLIGHTS

The next day he wrote a letter complaining about lack of cooperation.

WSJ: Cello's Golden Age Comes to a Close | J��nos Starker | By Stuart Isacoff