Which characters can I use for complex passcodes?
Depending on the app/situation, the acceptable password characters will vary. For example, when entering an email password or an iTunes password, you can enter in any of the characters available to you within iOS. 

For a phone lock passcode, you must use a 4-digit numerical code to lock the phone. It does not accept other options. 

Various other programs, such as 1Password, also accept their own set of characters although this software applies to the first part, which is that it accepts whichever characters are available to you in iOS.