Any complex number can be written in the form where is the imaginary unit and and are real numbers. Then the imaginary part of , usually denoted or , is just the value . Note in particular that the imaginary part of every complex number is real.
Geometrically, if a complex number is plotted in the complex plane, its imaginary part is its -coordinate (ordinate).
A complex number is real exactly when .
The function can also be defined in terms of the complex conjugate of : . (Recall that if , ).
- . Note in particular that is not in general a multiplicative function, for arbitrary complex numbers .