buy iphone in United states and use it in quebec city ?

Keep in mind that should you need warranty service, you will need to physically return the phone to the United States to get that service.

Buy the phone in the country in which you intend to use it.

In addition to AC and TP's comments, you have the problem of a carrier locked iPhone not working in Canada...you will probably have to look at an unlocked iPhone unless you know your carrier is the same as in the US - and will they transfer the purchase contract to Canada?

There are many reasons to buy the iPhone in Canada, where you live, rather than deal with all of the potential problems.