TOPICS
Complex Plane
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 
.
See also
Affine Complex Plane, Argand Diagram, Bergman Space, C-*, Cartesian Plane, Complex Projective Plane, Euclidean Plane, Extended Complex Plane, Imaginary Axis, Isotropic Line, Left Half-Plane, Lower Half-Disk, Lower Half-Plane, Punctured Plane, Real Line, Right Half-Plane, Upper Half-Disk, Upper Half-Plane Explore this topic in the MathWorld classroomExplore with Wolfram|Alpha
References
Courant, R. and Robbins, H. "The Geometric Interpretation of Complex Numbers." §5.2 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 92-97, 1996.Krantz, S. G. "The Topology of the Complex Plane." §1.1.5 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 3-5, 1999.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 23, 1986.Referenced on Wolfram|Alpha
Complex PlaneCite this as:
Weisstein, Eric W. "Complex Plane." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComplexPlane.html