It would be TOTALLY illogical for a certain race to exist together with a non-magical race, becouse in early ages, the magical ones would've slaughtered the non-magical ones, just like the sapiens did with the Neanderthals, and the Sapiens weren't even magical! No, it must be learned! Further, how about having all sorts of totally different techniques for different magics?
And Magic HAS to be complex, else everybody could find out how to work with it XD
Edit: An idea has spawned from the electrical circuit that is my brain: Every person has their own weapon, resembling who they are in magical terms, the weapon shapes do not realy matter atm, but it can be anything, anyway, these weapons are invisible, and can be summoned, and can't hurt things from that specific world (except magic), the weapons are summoned by focussing on the weapon, and shaping it with your hands in quick, striking movements for hard things (such as the poles, or the cutting blades) and slow, flowing moves for softer parts (for example the whole of a whip except the handle) then, they grab the weapon out of the air, right where them made it, and then, they make ritualistic movements, but the only thing they're doing is cutting open a way to one of the magical worlds, where they can draw their energy from, in other words, the weapon can only cut a portal which can be passed by both magic and object, but it is not adviced to go in there, as magic is in a chaotic state there, and would tear you apart as soon as you enter, further, after the portal is made (which is also invisible) they throw away their weapons, which disapear as soon as they let go, (realy, not just invisible) and then they pull out the magic with their hands (just away from the portal, if they do this uncarefully, they might lose their fingertips through the portal) and they can controll it, so it isn't in such a chaotic state anymore.
Also, instead of taking out the magic, they can also put their weapon in it (the invisible one) to make it physical, however, it can't cut holes anymore then, and you'll have to break the weapon to make it disapear, so you can summon it in it's invisible shape again.
So, what do you think? (except for it lacking paragraphs XD)