It is not very difficult to memorize random strings of arbitrary characters. I use a password manager to manage most of my accounts, but the important ones, like banks and email, I keep in my head. I use my password manager to generate a 15 character string of alpha+numeric+symbols. The symbols would kind of make it hard, except that in my head they are just upper-case numbers, mostly (shift-7, not ampersand). And in any case they are just positions on a keyboard (God help me if I need to enter one from my cell phone).

To memorize, just copy it into your favorite text editor, then type it 25 times in a row and delete. If you are paranoid, make sure you use a text editor that does not store temp files. Do not save this password anywhere. Set a timer and do it again an hour later, then again the next day. 10 minutes of your time and you have a password in your head. I can keep 10-20 of these at a time, maybe more since I seem to be able to type older ones from years ago.

I don't consider myself to have a great memory. I can barely remember lyrics to songs I've listened to dozens of times and it takes me hours and hours to memorize lines for plays. But I started doing this for passwords ten years ago and it is very reliable.