So what exactly is a complex number?

[Roy Smith]

Boris Borcic <bborcic at gmail.com> wrote:
> Complex numbers are like a subclass of real numbers 

I wouldn't use the term "subclass".  It certainly doesn't apply in the same 
sense it applies in OOPLs.  For example, you can't say, "All complex 
numbers are real numbers".  In fact, just the opposite.

But, it's equally wrong to say, "real numbers are a subclass of complex 
numbers", at least not if you believe in LSP 
(http://en.wikipedia.org/wiki/Liskov_substitution_principle).  For example, 
it is true that you can take the square root of all complex numbers.  It is 
not, however, true that you can take square root of all real numbers.

Don't confuse "subset" with "subclass".  The set of real numbers *is* a 
subset of the set of complex numbers.  It is *not* true that either reals 
or complex numbers are a subclass of the other.