In I Wanna Lockpick, I have an interest in the gimmick of twisting door requirements using imaginary master keys. I'll describe how it works here…

By default, a door with no copy labels has 1 real copy and 0 imaginary copies. If a door has no copies, it is destroyed. Under normal circumstances, a door’s copy count can only be decreased, either by using the required keys, or by using a master key. However, a negative master key can be used to add real copies to a door.

But imaginary numbers add an extra dimension of weirdness to door copies. If you apply an imaginary negative master key to a door, it gains an imaginary copy instead. An imaginary copy will have the same key requirement(s), but for imaginary keys instead (or real keys, if the lock was already imaginary). You can use the Lens of Truth to switch between opening real or imaginary copies.

To complicate the matter even further, applying a positive imaginary master key will open a nonexistent imaginary copy of the door, pushing the i-copy count into the negatives. A negative imaginary copy of a positive, real door, when seen in i-view, would become a negative, imaginary door. While non-master keys can only decrease the copy count, master keys can change the copy count no matter what, so long as the door doesn't hit 0+0i copies.

. . . That was certainly quite the writing. Apologies if this doesn't make sense to anyone who hasn't played I Wanna Lockpick, or hasn't heard about imaginary numbers.