Are all real numbers complex?

It only matters when you are looking into the algebraic structures and realize that it's just not appropriate to add a complex number to a real number (I'll avoid talking about multiplication right now). It's more appropriate to map the real number into a complex number first, and then add the two complex numbers. read more

In the special case that b = 0 you get pure real numbers which are a subset of complex numbers. I read that both real and imaginary numbers are complex numbers so I am a little confused with notations. What then is the purpose of saying something is a member of the reals or a member of complex if real numbers are also part of the complex numbers. read more

Yes all Real Numbers ([math]\mathbb{R}[/math]) are also Complex Numbers ([math]\mathbb{C}[/math]), in the same way that all Bananas are also fruits. This is because the Real Numbers are a subset of the Complex Numbers ([math]\mathbb{R}\subset\mathbb{C}[/math]). read more

A complex number is a number of the form a + bi, where a and b are real numbers and i is the principal square root of -1. In the special case where b=0, a+0i=a. Hence every real number is also a complex number. And in the special case where a=0, we call those numbers pure imaginary numbers. read more