Hi , my dealer just replaced the valvetronic motor after a few mintues of driving the car started shaking like crazy , went back and the computer is saying cylinder 4 misfire , everything was just fine before , my question is if he did the damage , i see the coil is cut in half

even he thrown it across the room i doubt he could split it in half lol
it not uncommon that these coil just fail or explode
make sure the plug is nice n tight then I would suggest to switch it to another cylinder, if the misfire follow change all of them to avoid futur headache

I used to have an e90 and my coils blew on me

I just went and bought 6 coils and spark plugs(since I was there) online and did it myself, if one went out the other could be soon so just do all to avoid future hassl.

I'm not much of a mechanic but there are some simple DIY youtube videos on how to change them.

Don't by the parts at BMW

These cars in stock form usually will make it a good while without issue, but inevitably they will fail. I currently have a 11’ 335i and I’m on my second set of coils since I purchased it last year. Furthermore had to do water pump/thermostat, valve cover and gasket and the oil filter housing gasket. Once those things are done these cars hold up exceptionally well to abuse.