Hi Tdano1, Welcome to All Things Plants!
I was not familiar with a plant by the name of Zanzibar Gem so I googled and I see that it is the plant many know by the common name of "ZZ Plant" due to the zig zag foliage:
ZZ Plant (Zamioculcas zamiifolia)
I live in Florida where the ZZ plant is grown outdoors as a landscape shrub but it is a very hardy plant and if it gets the proper light and moisture, it should do well for you as an indoor plant. The ZZ plant is drought tolerant so you don't want to keep the soil too wet or soggy ... or the roots and bulbs will rot. Cutting through those thick roots to separate your plant into two or more plants shouldn't do any harm at all ... that is one way of propagating the ZZ, by dividing the rootball into separate sections. And, yes, you can also propagate the plant by leaf cuttings. I stuck leaves in a vase of water one time and sat the vase in my kitchen, replacing the water about once a week so it didn't go stagnant; eventually I noticed bulbs and roots had formed at the base of the stems.
You can read more information about the plant at these sites:
http://tropicalplantrentals.co...
http://www.yates.com.au/garden...
http://www.vanlier.co.nz/shop/...
