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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Complex conjugate ： ウィキペディア英語版 Complex conjugate In mathematics, the complex conjugate of a complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of 3 + 4''i'' is 3 − 4''i''. In polar form, the conjugate of $\backslash rho\; e^$ is $\backslash rho\; e^$. This can be shown using Euler's formula. Complex conjugates are important for finding roots of polynomials. According to the complex conjugate root theorem, if a complex number is a root to a polynomial in one variable with real coefficients (such as the quadratic equation or the cubic equation), so is its conjugate. == Notation == The complex conjugate of a complex number $z$ is written as $\backslash overline\; z$ or $z^$ *\!. The first notation avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of the complex conjugate. The second is preferred in physics, where dagger is used for the conjugate transpose, while the bar-notation is more common in pure mathematics. If a complex number is represented as a 2×2 matrix, the notations are identical. In some texts, the complex conjugate of a previous known number is abbreviated as "c.c.". For example, writing $e^+c.c.$ means $e^+e^$ 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「Complex conjugate」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.