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...r by [[William Rowan Hamilton]] in 1837; this construction is explained [[Complex number#Formal definition|later in this article]]. ...i</math>. In this way, the real number <math>a</math> is considered as the complex number <math>a + 0i</math> whose imaginary part is zero.

...s]], while unknown variables <math>x</math> are [[real number|real]] or [[complex number|complex]] numbers.

In [[complex analysis]], a field of [[mathematics]], a [[complex number|complex]]-valued [[function (mathematics)|function]] ''f'' of a complex var

For example, the field of [[complex number]]s '''C''' is an extension of the field of [[real number]]s '''R'''.

...ysics]], the word '''scalar''' is often used to refer simply to a real or complex number. ...matrix|rotation]]). The [[determinant]] of a unitary transformation is a complex number of absolute value unity, that is, the determinant of a unitary transformati

...d to work for all quadratic polynomials, but sometimes the roots will be [[complex number]]s even when every other part of the problem deals only with [[real number

...amous bridge inscription is told at some length in Conway and Smith (see [[Complex number#Further reading]] for a full reference) where it is described as "one of th

{{Image|Complex number.png|right|350px| Complex number ''z'' &equiv; ''r'' exp(''i''&theta;) multiplied by ''i'' gives <i>z'</i> <

...governed by [[modular arithmetic|arithmetic modulo 2]]. Polynomials with complex number coefficients or coefficients modulo 2 behave similarly to polynomials with

Given some [[complex number|complex-valued]] function <math>\scriptstyle f\,:\,\mathbb{R} \rightarrow \

Created [[Complex number/Draft]] [[User:David Tribe|David Tribe]] 19:30, 6 May 2007 (CDT)

...ext of real numbers. There are natural multiplication operations on the [[complex number]]s, [[matrix|matrices]], [[tensor]]s, [[sequence]]s, and [[function]]s.

This definition of continuity extends directly to functions of a [[complex number|complex]] variable.

...the ground field has been extended from the real numbers to the field of [[complex number]]s and later to arbitrary [[field]]s. In the second place notions of abstra

*[[Complex number]] (approved)

...like [[integer]]s, [[rational number|rational]], [[real number|real]] or [[complex number|complex]] numbers. Still it is important to understand that calculations wi

...ath> and <math>G</math> are established, the function can be iterated even complex number of times. ...omorphic function can be iterated any number <math>n</math> of times, even complex number of times.

...d, but applying them requires sophisticated knowledge of arithmetic with [[complex number]]s. There are no analogous formulas for solving polynomial equations of or

Some simple examples of sequences of the natural, [[real numbers|real]], or [[complex number]]s include (respectively)

...the imaginary number 2i as the base, having the unusual feature that every complex number can be represented with the digits 0, 1, 2, and 3, without a sign.