The argument of z, denoted by arg(z), is just another name used for representing the angle θ which is multi-valued with a period of 2π . Thus, if θ is one value of arg(z), the other values are given by arg(z) = θ + 2πn, where n is any integer. If r = 0, then θ can be set to any real value. However, if r = 0, then in order to get a unique value, θ must be limited to an interval of size 2π which is traditionally chosen as being used for taking the

order to correctly calculate the location and value of θ . Fortunately, many modern programming languages, such as C#, avoid having to directly handle this problem by simply using the atan2(y/x) function, which has separate arguments for both the x and the y values. As a result, the output from the function atan2(y/x) consists of a unique value within the interval (−π ,π ] and will be henceforth referred to as the principal value of θ .