Imaginary part
From AoPSWiki
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 , 
).
Examples
-
. Note in particular that 
is not in general a multiplicative function, 
for arbitrary complex numbers 
.
