01
f(z) = arg(z)
Colored density plot of the argument of z (= phase of z). The argument of a complex number varies between -Pi and Pi. Positive real numbers have the argument 0 (black). The function arg(z) is discontinuous along the negative real axis. As you cross the negative real axis from above, the value of arg(z) jumps from +Pi to -Pi. Sometimes it is useful to allow all real numbers as argument values. This means that the argument is multi-valued as a "function" of z: Whenever one goes around the origin, the value of the argument increases by 2Pi.