In mathematics (particularly in complex analysis), the argument is a multi-valued function operating on the nonzero complex numbers. With complex numbers z visualized as a point in the complex plane, the argument of z is the angle between the positive real axis and the line joining the point to the origin, shown as φ in figure 1 and denoted arg z. To define a single-valued function, the principal value of the argument (sometimes denoted Arg z) is used. It is often chosen to be the unique value of the argument that lies within the interval (–π, π]. == Definition == An argument of the com...