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Suppose that the complex number z is represented by the point P in the complex plane. The argument of z, denoted by arg z, is the angle θ (in radians) that OP makes with the positive real axis Ox, with the angle given a positive sense anticlockwise from Ox. As with polar coordinates, the angle θ may be taken so that 0≤arg z<2π. Usually, however, the angle θ is chosen so that −π<arg zπ. Sometimes, arg z is used to denote any of the values θ+2nπ, where n is an integer. In that case, the particular value that lies in a certain interval, specified or understood, such as [0, 2π) or (−π, π], is called the principal value of arg z.

Subjects: Mathematics.

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