The definition of complex, real and pure imaginary number is as follows:
[tex]A \ \mathbf{complex \ number} \ is \ written \ in \ \mathbf{standard \ form} \ as:\\ \\ \ (a+bi) \\ \\ where \ a \ and \ b \ are \ real \ numbers. \ If \ b=0, \ the \ number \ a+bi=a \\ is \ a \ \mathbf{real \ number}. \ If \ b\neq 0, \ the \ number \ (a+bi) \ is \ called \ an \\ \mathbf{imaginary \ number}. \ A \ number \ of \ the \ form \ bi, \ where \ b\neq 0, \\ is \ called \ a \ \mathbf{pure \ imaginary \ number}[/tex]
The absolute value of this number is given by:
[tex] |a+bi|=\sqrt{a^{2}+b^{2}} [/tex]
So, the absolute value of a complex number represents the distance between the origin and the point in the complex plane. On the other hand, the absolute value of a real number means only how far a number is from zero without considering any direction.
