complex variable

a variable to which complex numbers may be assigned as value.
[1875-80]

* * *

In mathematics, a variable that can take on the value of a complex number.

In basic algebra, the variables x and y generally stand for values of real numbers. The algebra of complex numbers (complex analysis) uses the complex variable z to represent a number of the form a + bi. The modulus of z is its absolute value. A complex variable may be graphed as a vector from the origin to the point (a,b) in a rectangular coordinate system, its modulus corresponding to the vector's length. Called an Argand diagram, this representation establishes a connection between complex analysis and vector analysis. See also Euler's formula.

* * *


Universalium. 2010.

Look at other dictionaries:

  • complex variable — com′plex var′iable n. math. a variable to which complex numbers may be assigned as value • Etymology: 1875–80 …   From formal English to slang

  • complex variable — noun : a number or expression of the form x+iy where i=√‒̅1 and x and y are in general variables * * * Math. a variable to which complex numbers may be assigned as value. [1875 80] …   Useful english dictionary

  • Complex dynamics — is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions. Contents 1 Techniques[1] 2 Parts 3 See also …   Wikipedia

  • Complex analysis — Plot of the function f(x)=(x2 1)(x 2 i)2/(x2 + 2 + 2i). The hue represents the function argument, while the brightness represents the magnitude. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch …   Wikipedia

  • Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… …   Wikipedia

  • Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics …   Wikipedia

  • Complex logarithm — A single branch of the complex logarithm. The hue of the color is used to show the arg (polar coordinate angle) of the complex logarithm. The saturation (intensity) of the color is used to show the modulus of the complex logarithm. The page with… …   Wikipedia

  • variable — variability, variableness, n. variably, adv. /vair ee euh beuhl/, adj. 1. apt or liable to vary or change; changeable: variable weather; variable moods. 2. capable of being varied or changed; alterable: a variable time limit for completion of a… …   Universalium

  • Complex instruction set computing — A complex instruction set computer (CISC) (  /ˈsɪs …   Wikipedia

  • Complex data type — Some programming languages provide a complex data type for complex number storage and arithmetic as a built in (primitive) data type. In some programming environments the term complex data type (in contrast to primitive data types) is a synonym… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.