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In mathematics, arg is a function operating on complex numbers (visualized in a complex plane). It gives the angle between the positive real axis to the line joining the point to the origin, shown as in figure 1, known as an argument of the point. ==Definition== An argument of the complex number , denoted , is defined in two equivalent ways: #Geometrically, in the complex plane, as the angle from the positive real axis to the vector representing . The numeric value is given by the angle in radians and is positive if measured counterclockwise. #Algebraically, as any real quantity such that :: :for some positive real . The quantity is the ''modulus'' of , denoted ||: :: The names ''amplitude'' for the modulus and ''phase''〔Dictionary of Mathematics (2002). ''phase''.〕 for the argument are sometimes used equivalently. Under both definitions, it can be seen that the argument of any (non-zero) complex number has many possible values: firstly, as a geometrical angle, it is clear that whole circle rotations do not change the point, so angles differing by an integer multiple of radians (a complete circle) are the same. Similarly, from the periodicity of and , the second definition also has this property. 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「Argument (complex analysis)」の詳細全文を読む スポンサード リンク
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