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...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.

**The [[rational number|rational]], [[real number|real]] and [[complex number|complex]] numbers each form commutative rings.

In the case of a [[complex number|complex]]-valued function ''ƒ''(ξ), ''Fourier's theorem'' states that a

However, over the [[complex number]]s we can write

This is some material that used to be in the [[complex number]] article, but I felt an entire article on the fundamental theorem of algeb

...ressed in radicals using only real numbers. But finding the cube root of a complex number can be accomplished in polar form, so changing the form of the complex numb

Galois expressed his theory in terms of polynomials and [[complex number|complex numbers]], today Galois theory is usually formulated using general

...value of <math>f(x)</math> within the [[real number]]s &mdash; but using [[complex number]]s a value can be found, as will be discussed further below. To find the logarithm of a complex number <math>a + bi</math>, it is convenient to express the number in polar coordi

In order to prove the last relation we write a complex number in polar form

...not a mere copyedit and so did require a new version to be approved. In [[Complex number]] this was a typo -nothing more thasn that-and the policy I am following is

...tended in several directions. Perhaps the most natural extension are the [[complex number]]s, which contain solutions to all [[polynomial]] equations, and, unlike th

...have deleted essentially everything I wrote about complex analysis in the complex number article. That's fine, as I really think it belongs in another article, and Ekhem, I noticed that my modest reworking of [[complex number]] was reverted too (see talk).. While I am fully open to change (and beggin

for any [[complex number]] <math>\scriptstyle z</math>. Equivalently, it may be defined as the [[inv

...upon frequency, as normally expressed using an impedance represented by a complex number.

...1843 theory of [[quaternions]]. The quaternions are a generalization of [[complex number]]s. They can be added and multiplied and thus form a structure that is now

{{Notice|Complex number|N|reapproval}}

...math>\mathbb{R}^n</math></font> for any [[natural number]] ''n''; or the [[complex number|complex plane]] or powers of it, <font style = "vertical-align: 13%"><math

...lisations of the rational numbers. Briefly, an ''algebraic number'' is any complex number that is a solution to some polynomial equation <math>\scriptstyle f(x)=0</m