Yes, many
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1 use is to describe a point in the plane. Say you have x=2 and y=11. and can be z=2+i11.
Use the link below to begin your investigation of the geometry of Ph3SnCl and the polar aprotic solvent DMSO (dimethyl sulfoxide).
electrical engineers and quantum mechanics use them.
I'm not sure about how to use complex numbers to do this, but I've posted a link to a pretty neat website about Synthetic Division.
using contraction and expansion