# Signum

The function of a real variable $x$ which is equal to $1$ if $x$ is positive, equal to 0 if $x$ is zero and equal to $-1$ if $x$ is negative. Notation: $\operatorname{sgn} x$ or $\operatorname{sign} x$. Thus, \begin{equation*} \operatorname{sgn} x = \begin{cases} \ \ \,\,1\quad \text{if } x>0,\\ \ \ \,\,0\quad \text{if } x=0,\\ -1\quad \text{if } x<0.\\ \end{cases} \end{equation*}
The signum function is usually extended to the complex plane by $\operatorname{sgn} z = z / |z|$ if $z\ne0$ (and $\operatorname{sgn} 0=0$). Thus, it measures the angle of the ray from the origin on which $z$ lies.