Normally this isn't much of a problem. However, modems are very, very sensitive to noise. Every time the equipment recharges itself, it causes a faint noise on the phone line that can disrupt a modem enough to cause it to hang up. If you suspect this is a problem, temporarily disconnect phone accessories before you get on the Internet. This is not the case at all.
Some modems can tolerate phone noise very well, while others are almost useless.
We have found that RPI and WinModems often work very poorly. Most modems have special electronic components that do 'error correction'. Somebody got the bright idea that they could make modems cheaper if they did away with these electronics components and replaced them with computer software. In theory this sounds good. You can spot these modems by looking on the box for a phrase similar to 'software error correction'.