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 .

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.