1. It is undefined. An easy way to see that it would be difficult to define it uniquely is to consider that the argument of a product is the sum of arguments, i.e: arg(z1z2) = arg(z1) + arg(z2) arg ( z 1 z 2) = arg ( z 1) + arg ( z 2) If we consider z1 = 0 z 1 = 0, we find: arg(0) = arg(0) + arg(z2) arg ( 0) = arg ( 0) + arg ( z 2) So therefore
The angle θ of a complex number's polar representation is its argument, z = a+ib. This is a multi-valued angle. If is the complex number z argument, then θ+2nπ, n is an integer, and will also be an argument of that complex number. The principal argument of a complex number, on the other hand, is the unique value of such that -πArg [z] is left unevaluated if z is not a numeric quantity. Arg [z] gives the phase angle of z in radians. The result from Arg [z] is always between and . Arg [z] has a branch cut discontinuity in the complex z plane running from to 0. Arg [0] gives 0. Arg can be used with Interval and CenteredInterval objects. » Arg automatically threads over
First, we recall the argument of a complex number 𝑧, written arg 𝑧, is the angle that 𝑧 makes with the positive real axis on an Argand diagram. And there are a few things worth pointing out about this definition. First, technically, it's not the angle that 𝑧 makes with the positive real axis on our Argand diagram.