Warhammer Arcane Magic (1995) is the expansion to Warhammer Battle Magic (1992), the magic supplement for Warhammer Fantasy Battles 4th Edition (1992). Both the Arcane and Battle Magic were reprised in the 5th Edition supplement Warhammer Magic (1995). Warhammer Magic tweaked a few things (both core magic rules and the wording on cards), but largely kept things the same.
The box set you have, Warhammer Arcane Magic, added Chaos Dwarf, Ice and Necromancy spells and added three Dark Magic spells (since Raise the Dead and Vanhel's Dance Macabre were moved from Dark to Necromancy). It should also have a bunch of magic items (84), a rulebook and a few tokens for fliers (4, I think). That was a great rulebook because it summarized all the magic lores and items in the back (in case you lost a card).
I prefer the 4th Edition magic boxes to the 5th Edition one, although 5th Edition is really quit similar and has one better rule (no casting spells during opponent's turn—otherwise, the magic phase just takes too long!).
To answer your question, yes—you need Battle Magic (or the Magic box set, which replaces both). You could get by with just the Battle Magic rulebook and a set of power cards, though, if you didn't want the magic items and spells in card form (you might also need the templates, but I think many of these were reprinted in White Dwarf and elsewhere).
updates and cleans some minis.
