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**imaginary unit wikipedia**: The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x 2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication.An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2 = −1. The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. Zero is considered to be both real and imaginary.The imaginary unit, represented by the lower-case letter $ i $ (or possibly $ j $, or even the Greek letter $ \iota $ [iota]), is the basis of the imaginary number line, or imaginary continuum. It is typically defined as a solution of the quadratic equation $ x^2+1=0 $, or equivalently, $ x^2=-1 $.The imaginary unit is often loosely referred to as the "square root of −1". However, there are in fact two square roots of −1 (just as there are two square roots of every real number), namely i and −i. Misuse of the imaginary unit may lead to difficulties. For a history of the imaginary unit, see Complex number: History.Actually it is not a problem to define \(-i\) as the imaginary unit. \(i\) is literally imaginary and does not exist in the real world. \(i\) is an abstract concept, and the complex number systems with \(i\) and \(-i\) as their imaginary units have the same properties.That is the use for which the imaginary unit was created. Square root of the imaginary unit. One might assume that a further set of imaginary numbers needs to be invented to account for the square root of i. However this is not necessary as it can be expressed as either of two complex numbers: [1] Indeed, squaring the right-hand side givesIn math, imaginary units, or , are numbers that can be represented by equations but refer to values that could not physically exist in real life.The mathematical definition of an imaginary unit is = −, which has the property × = = −.. The reason was created was to answer a polynomial equation, + =, which normally has no solution as the value of would have to equal -1.imaginary unit. Definition from Wiktionary, the free dictionary. Jump to navigation Jump to search. English . English Wikipedia has an article on: imaginary unit. Wikipedia . Noun . imaginary unit (plural imaginary units) (complex analysis) A complex number, usually denoted with i, ...In math, imaginary units, or [math]i[/math], are numbers that can be represented by equations but refer to values that could not physically exist in real life.The mathematical definition of an imaginary unit is [math]i = \sqrt{-1}[/math], which has the property [math]i \times i = i^2 = -1[/math].. The reason [math]i[/math] was created was to answer a polynomial equation, [math]x^2 + 1 = 0 ...This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.: You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in ...

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