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- ...addition]], subtraction, [[multiplication]], and division can be used with complex numbers. They also follow [[commutative property|commutative]], [[associati Complex numbers were invented to answer special equations that have [[exponent]]s i ...6 KB (917 words) - 00:53, 5 February 2017
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- ...vre's formula''', named after [[Abraham de Moivre]], states that for any [[complex number]] ''z'' and [[integer]] ''n'', ..., with <math>|z|e^{i.\arg z}</math> often being called the polar form of a complex number. ...985 bytes (158 words) - 09:05, 20 June 2017
- ...with [[Multiplicity (mathematics)|multiplicity]] greater than one) in the complex numbers. If the discriminant is smaller than zero, then there are two distinct [[complex number]]s. ...918 bytes (140 words) - 23:26, 12 July 2017
- ...addition]], subtraction, [[multiplication]], and division can be used with complex numbers. They also follow [[commutative property|commutative]], [[associati Complex numbers were invented to answer special equations that have [[exponent]]s i ...6 KB (917 words) - 00:53, 5 February 2017
- ...rong colors are for values close to zero and [[hue]] encodes the value's [[complex number|argument]]. [[File:Complex coloring.jpg|thumb|300px|upright=1.2|The coloring of the complex function-values used above: positive real values are presented in red.]] ...3 KB (534 words) - 10:42, 20 June 2017
- ...f(x)</math> with [[real]] or [[complex number|complex]] coefficients has a complex root. A root is a number ''x'' which gives a solution <math>f(x)=0</math>. * [[Complex analysis]] ...3 KB (574 words) - 23:27, 15 January 2016
- ===A more complex example=== ...2 KB (379 words) - 14:57, 30 April 2017
- ...ric domains supported often include [[real number|real]], [[complex number|complex]], [[interval (mathematics)|interval]], [[rational number|rational]], and a ...asily calculate the total possible error of an inexact arithmetic system. Complex number arithmetic is generally supported by allowing the [[imaginary unit]] ...3 KB (424 words) - 02:38, 27 March 2013
- ...=Thumbnail-of-Riemann Zeta.jpg.png|thumb|The Riemann zeta function, in the complex plane. The real part <math>\operatorname{Re}(s)</math> of the number is dra ...ction]], the [[Riemann zeta function]]. This function inputs and outputs [[complex number]] values. The inputs that give the output zero are called [[root (m ...2 KB (337 words) - 10:32, 20 June 2017
- == Complex Exponentiation == A complex number can also be taken to the power of another complex number. The relationship between imaginary numbers and trigonometry, which ...8 KB (1,393 words) - 01:43, 31 May 2017
- ...oid, the final combined result will be the same. This also works with more complex Monoids e.g. a map of word counts. ...729 bytes (116 words) - 19:01, 14 June 2016
- {{complex|date=January 2012}} ...915 bytes (111 words) - 07:20, 3 November 2013
- ...tput. An example of a multivalued function is the [[square root]]. Every complex number (except for 0), has two square roots. Example: <math>\sqrt{4}</math ...881 bytes (123 words) - 22:40, 23 March 2016
- ...number '''0''' is the "additive identity" for integers, real numbers, and complex numbers. For the real numbers, for all <math>a\in\Bbb{R},</math> ...r '''1''' is the "multiplicative identity" for integers, real numbers, and complex numbers. For the real numbers, for all <math>a\in\Bbb{R},</math> ...3 KB (425 words) - 19:31, 17 March 2013
- {{complex|date=January 2012}} ...846 bytes (137 words) - 09:46, 20 October 2014
- ===The real line and complex plane=== ...infty</math>. This is treated as addition to the [[real numbers]] or the [[complex numbers]]. It is the result of division by zero, or to indicate that a [[se ...6 KB (828 words) - 00:07, 11 November 2015
- ...such as the oxidation of sugar in the human body, through a series of very complex [[electron transfer]] processes.</ref> ...3 KB (389 words) - 08:00, 8 January 2015
- | <nowiki>|x|</nowiki> is the distance along the real line (or across the complex plane) between x and zero | [[Complex numbers]] ...8 KB (1,182 words) - 07:31, 3 November 2013
- ...mpedance.svg|200px|thumb|A graphical representation of the [[Complex plane|complex impedance plane]]]] (see the 2nd figure, "complex impedance plane") ...5 KB (850 words) - 06:03, 26 June 2016
- {{complex|date=May 2012}} ...1,002 bytes (151 words) - 20:37, 2 January 2014
- {{complex|date=May 2012}} ...1 KB (172 words) - 07:05, 3 November 2013
- ...[[complex number]]s. Every real number is a complex number, but not every complex number is a real number. ...6 KB (971 words) - 01:36, 21 August 2017
- In a synthesis reaction, two or more simple substances combine to form a more complex substance. ...e is simple hydrogen gas combined with simple oxygen gas to produce a more complex substance, such as water.<ref name="to react or not to react">[http://utahs ...5 KB (701 words) - 12:12, 4 June 2017
- ...e root is a [[complex number]]. For example, square root of '''-4''' is a complex number '''2''[[imaginary unit|i]]''''' :<math display="block">\sqrt{-4} = 2 ...3 KB (526 words) - 04:59, 30 June 2016
- {{complex|date=March 2012}} {{complex|date=March 2012}} ...3 KB (427 words) - 19:05, 27 March 2017
- {{complex|date=April 2012}} ...c energy, although this may not be helpful to those not familiar with more complex physics. ...3 KB (561 words) - 06:11, 16 June 2016
- {{complex|date=April 2012}} ...1 KB (154 words) - 07:17, 12 January 2015
- A [[real number|real]] or [[complex number]] is called a '''transcendental number''' if it cannot be found as a ...1 KB (199 words) - 20:58, 16 March 2013
- ...e given area, since the normal answer for the wave function is usually a [[complex number]]. The wave function concept was first introduced in the legendary [ ...1 KB (187 words) - 14:02, 12 November 2014
- === Complex numbers === ...rt and an ''imaginary'' part. Every type of number written above is also a complex number. ...14 KB (2,057 words) - 01:36, 21 August 2017
- {{complex|date=March 2012}} The Big O Notation is often used in identifying how complex a problem is (also known as the problem's [[complexity class]]). ...4 KB (700 words) - 14:03, 20 September 2015
- {{complex|date=April 2012}} ...1 KB (189 words) - 07:34, 13 September 2016
- {{complex|date=March 2012}} ...1 KB (200 words) - 15:36, 12 March 2013
- {{Complex|date=June 2012}} ...1 KB (199 words) - 07:36, 12 January 2015
- {{complex|date=September 2011}} ...1 KB (222 words) - 13:32, 21 June 2017
- ...he model. Since individual outcomes might be of little practical use, more complex ''events'' are used to characterize groups of outcomes. The collection of a ...2 KB (250 words) - 19:23, 8 November 2016
- {{complex|date=June 2012}} ...1 KB (195 words) - 08:01, 30 March 2017
- <!-- comment out really complex information ...2 KB (231 words) - 00:24, 15 February 2014
- {{complex|date=June 2014}} ...1 KB (200 words) - 00:02, 2 January 2015
- {{complex|date=July 2012}} ...1 KB (198 words) - 04:44, 5 May 2016
- ...e [[fundamental theorem of algebra]], in the form of a generalisation in [[complex numbers]]. ...1 KB (269 words) - 18:04, 4 May 2016
- * some of the roots may be [[complex number]]s ...2 KB (288 words) - 19:05, 9 March 2015
- Wavelet is (complex) function from the [[Hilbert space]] <math>\psi \in L^{2}(\mathbb{R})</math ...2 KB (280 words) - 16:47, 26 March 2017
- ...[[rational numbers]] by including square roots of positive numbers. The [[complex numbers]] are a closure of the real numbers by including square roots of ne ...2 KB (271 words) - 03:33, 15 January 2015
- ...z'')) is an [[wikt:extend|extension]] of the [[factorial]] function to all complex numbers except negative, integers. The argument of the function is shifted ...lex numbers]]. But it is not defined for negative integers and zero. For a complex number whose real part is not a negative integer, the function is defined b ...8 KB (1,133 words) - 09:45, 26 June 2017
- * [[Complex number]] ...2 KB (303 words) - 17:40, 15 February 2016
- {{complex}} ...2 KB (308 words) - 18:29, 1 November 2016
- {{complex|date=October 2011}} ...^\infty {\alpha \choose i} x^i\quad\mbox{ for all } |x| < 1 \mbox{ and all complex } \alpha\!</math> ...7 KB (1,090 words) - 18:10, 19 October 2014
- {{Article issues|complex=July 2013|wikify=April 2009}} ...2 KB (282 words) - 23:05, 31 May 2017
- {{complex}} ...2 KB (249 words) - 16:54, 23 January 2015
- ...ically numbers that cannot be square rooted and get a real result. Every [[complex number]] except 0 has 2 square roots. For example: −1 has two square roots. ...2 KB (290 words) - 09:33, 2 February 2016