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In mathematics , the argument of a complex number z, denoted arg, is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as φ {\displaystyle \varphi } in Figure 1. It is a multi-valued function operating on the nonzero complex numbers.To define a single-valued function, the principal value of the argument is used. It is often chosen to be the unique value of the argument that lies within the interval.
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