Download Wolfram Notebook

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 classroom

Explore 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 Plane

Cite this as:

Weisstein, Eric W. "Complex Plane." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComplexPlane.html

Subject classifications