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An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit ,〔''j'' is often used in Engineering〕 which is defined by its property .〔 〕 The square of an imaginary number is . For example, is an imaginary number, and its square is . Except for 0 (which is both real and imaginary), imaginary numbers produce negative real numbers when squared. An imaginary number can be added to a real number to form a complex number of the form , where the real numbers and are called, respectively, the ''real part'' and the ''imaginary part'' of the complex number.〔Both the real part and the imaginary part are defined as real numbers.〕 Imaginary numbers can therefore be thought of as complex numbers whose real part is zero. The name "imaginary number" was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless. The term "imaginary number" now means simply a complex number with a real part equal to , that is, a number of the form . ==History== (詳細はHeron of Alexandria is noted as the first to have conceived these numbers, Rafael Bombelli first set down the rules for multiplication of complex numbers in 1572. The concept had appeared in print earlier, for instance in work by Gerolamo Cardano. At the time, such numbers were poorly understood and regarded by some as fictitious or useless, much as zero and the negative numbers once were. Many other mathematicians were slow to adopt the use of imaginary numbers, including René Descartes, who wrote about them in his ''La Géométrie'', where the term ''imaginary'' was used and meant to be derogatory.〔, discusses ambiguities of meaning in imaginary expressions in historical context.〕 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).〔 〕 In 1843 a mathematical physicist, William Rowan Hamilton, extended the idea of an axis of imaginary numbers in the plane to a three-dimensional space of quaternion imaginaries. With the development of quotient rings of polynomial rings, the concept behind an imaginary number became more substantial, but then one also finds other imaginary numbers such as the j of tessarines which has a square of . This idea first surfaced with the articles by James Cockle beginning in 1848.〔James Cockle (1848) "On Certain Functions Resembling Quaternions and on a New Imaginary in Algebra", London-Dublin-Edinburgh Philosophical Magazine, series 3, 33:435–9 and Cockle (1849) "On a New Imaginary in Algebra", Philosophical Magazine 34:37–47〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Imaginary number」の詳細全文を読む スポンサード リンク
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