The complex plane is the plane of complex numbers spanned by the vectors 1 and 
, where 
is the imaginary number.
Every complex number corresponds to a unique point in the complex plane. The line
in the plane with 
is the real line. The complex plane is sometimes called
the Argand plane or Gauss plane, and a plot of complex
numbers in the plane is sometimes called an Argand
diagram.
The complex plane together with the point at infinity 
is known as the Riemann
sphere or extended complex plane and denoted 
or 
. However, the notation 
is also used to denote the punctured
plane 
.
