There is more to it. Vectors typically don't have multiplication defined. Complex numbers form a field and that is a major extra feature. Multiplication and division I'd defined on them.
If this property is not needed one can make do with 2d vectors instead.
There are 4d and 8d analogues as well. Hamilton started an ambitious program to base mathematics of nature on the basis of the 4d ones -- quarternions
If this property is not needed one can make do with 2d vectors instead.
There are 4d and 8d analogues as well. Hamilton started an ambitious program to base mathematics of nature on the basis of the 4d ones -- quarternions