Yes I do believe that it is extremely inappropriate to do hoaxes regarding death. Death is a really sensitive and serious subject matter and should not be a part of any hoax whether it is on the Internet or not. Some hoaxes are funny and are not serious but this is not.
In this day and age where information is transmitted instantaneously, a rumored death spread through the Internet is an unnecessary evil. The fire that can be fueled by a death hoax, especially if it's a celebrity can create havoc and unnecessary chatter on social media such as Facebook or Twitter. For those who fans of a particular celebrity, the news of his or her death can be devastating, only to find out it's untrue. These hoaxes cause stress.
In recent days people seem to die twice especially celebrity. These Internet hoaxes have killed many celebrities recently. Alot of fans who follow celebrity closely tend to believe in such hoaxes and these things go viral with the advancement in social media. Fans and close relatives are drawn into confusion with these false news.
False death Internet hoaxes are inappropriate. News travels so fast nowadays, one false statement is taken as truth before any other reaction can be made. We have to remember that celebrities are people, and they have families and friends just like the rest of us. A false notification of death would be devastating to any of us.