Editing Imaginary number (section)

==History==
{{Main|History of complex numbers}}
[[File:Complex conjugate picture.svg|right|thumb|An illustration of the complex plane. The imaginary numbers are on the vertical coordinate axis.]]
Although the Greek [[mathematician]] and [[engineer]] [[Heron of Alexandria]] is noted as the first to present a calculation involving the square root of a negative number,<ref>{{cite book |title= Fivefold Symmetry |edition= 2 |first= István |last= Hargittai |publisher= World Scientific |year= 1992 |isbn= 981-02-0600-3 |page= 153 |url= https://books.google.com/books?id=-Tt37ajV5ZgC&pg=PA153}}</ref><ref>{{cite book |title= Complex Numbers: lattice simulation and zeta function applications |first= Stephen Campbell |last= Roy |publisher= Horwood |year= 2007 |isbn= 978-1-904275-25-1 |page= 1 |url= https://books.google.com/books?id=J-2BRbFa5IkC}}</ref> it was [[Rafael Bombelli]] who first set down the rules for multiplication of [[complex number]]s in 1572. The concept had appeared in print earlier, such as in work by [[Gerolamo Cardano]]. At the time, imaginary numbers and negative numbers were poorly understood and were regarded by some as fictitious or useless, much as zero once was. Many other mathematicians were slow to adopt the use of imaginary numbers, including [[René Descartes]], who wrote about them in his ''[[La Géométrie]]'' in which he coined the term ''imaginary'' and meant it to be derogatory.<ref>[[René Descartes|Descartes, René]], ''Discours de la méthode'' (Leiden, (Netherlands): Jan Maire, 1637), appended book: ''La Géométrie'', book three, p. 380. [http://gallica.bnf.fr/ark:/12148/btv1b86069594/f464.item.zoom From page 380:] ''"Au reste tant les vrayes racines que les fausses ne sont pas tousjours reelles; mais quelquefois seulement imaginaires; c'est a dire qu'on peut bien tousjours en imaginer autant que jay dit en chasque Equation; mais qu'il n'y a quelquefois aucune quantité, qui corresponde a celles qu'on imagine, comme encore qu'on en puisse imaginer trois en celle cy, x<sup>3</sup> – 6xx + 13x – 10 = 0, il n'y en a toutefois qu'une reelle, qui est 2, & pour les deux autres, quoy qu'on les augmente, ou diminue, ou multiplie en la façon que je viens d'expliquer, on ne sçauroit les rendre autres qu'imaginaires."'' (Moreover, the true roots as well as the false [roots] are not always real; but sometimes only imaginary [quantities]; that is to say, one can always imagine as many of them in each equation as I said; but there is sometimes no quantity that corresponds to what one imagines, just as although one can imagine three of them in this [equation], x<sup>3</sup> – 6xx + 13x – 10 = 0, only one of them however is real, which is 2, and regarding the other two, although one increase, or decrease, or multiply them in the manner that I just explained, one would not be able to make them other than imaginary [quantities].)</ref><ref name="Martinez">{{Citation |first= Albert A. |last= Martinez |title= Negative Math: How Mathematical Rules Can Be Positively Bent |location= Princeton |publisher= Princeton University Press |year= 2006 |isbn= 0-691-12309-8}}, discusses ambiguities of meaning in imaginary expressions in historical context.</ref> The use of imaginary numbers was not widely accepted until the work of [[Leonhard Euler]] (1707–1783) and [[Carl Friedrich Gauss]] (1777–1855). The geometric significance of complex numbers as points in a plane was first described by [[Caspar Wessel]] (1745–1818).<ref>{{cite book
 |title= A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space
 |first= Boris Abramovich
 |last= Rozenfeld
 |publisher= Springer
 |year= 1988
 |isbn= 0-387-96458-4
 |chapter= Chapter 10
 |page= 382
 |chapter-url= https://books.google.com/books?id=DRLpAFZM7uwC&pg=PA382}}
</ref>

In 1843, [[William Rowan Hamilton]] extended the idea of an axis of imaginary numbers in the plane to a four-dimensional space of [[quaternion#Definition|quaternion imaginaries]] in which three of the dimensions are analogous to the imaginary numbers in the complex field.