How to recover forgotten iMac username and password?

Click If you forgot your Mac login password or if you forgot your AppleID click If you forgot your Apple ID password

Going off the rails and doing a re-install will NOT solve the problem. By doing a simple Google search ( Mac forgot login password) you would have found the first link and saved yourself quite a bit of time.

Okay, your next step is a phone call to AppleCare ( click AppleCare Contact Info to get the phone number for your area ) .

Also, I STRONGLY recommend that you get yourself an app for your phone and/or tablet for passwords. Something like 1Password. 1 Password (and other similar products) are great because no-one can remember all of their logins and passwords these days particularly with more increased security. If you happen to use an iPhone look in the App Store for password "password manager" and you will find a number of apps. I just happen to use 1Password (and I like it) but you may find others you prefer.