Woah! Poor choice of words my friend. I understand the point you're trying to make, but the termreal numberis a well defined concept in mathematics (the set of real numbers is denoted byR)and any number with an imaginary part is most certainly NOT in the set of real numbers (denoted byC).

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)