Yep, had that argument many times. Learnt it a long time ago when first in IT - make the password requirements too complex or change them too often, and people write them down on the desk, keyboard, post-it note or God knows where else. A bit of user education and sensible policy goes a long way to helping overall security.
Like you, I have a very complex password for banking and the like, which is written down nowhere and has nothing to do with me whatsoever so can't be guessed, easily brute forced or dictionary attacked. Have a simple one for other things where complexity is pointless as half the crap systems store the things in plaintext anyway.

