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Complex Plane


ComplexPlane

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the complex plane. The line in the plane with i=0 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 C union {infty} is known as the Riemann sphere or extended complex plane and denoted C^* or C^^. However, the notation C^* is also used to denote the punctured plane C-{0}.


See also

Affine Complex Plane, Argand Diagram, Argand Plane, 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

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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 Web Resource. https://mathworld.wolfram.com/ComplexPlane.html

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