Woah! Poor choice of words my friend. I understand the point you're trying to make, but the term real number is a well defined concept in mathematics (the set of real numbers is denoted by R)and any number with an imaginary part is most certainly NOT in the set of real numbers (denoted by C).
All real numbers are in the set of complex numbers I should probably add (since a real number is just a complex number with b=0)