The sign of a real number, also called sgn or signum, is for a negative number (i.e., one with a minus sign ""), 0 for the number zero, or for a positive number (i.e., one with a plus sign ""). In other words, for real ,

(1)

For real , this can be written

(2)

and satisfies

(3)

for real can also be defined as

(4)

where is the Heaviside step function.

The sign function is implemented in the Wolfram Language for real as Sign[x]. For nonzero complex numbers, Sign[z] returns , where is the complex modulus of .

can also be interpreted as an unspecified point on the unit circle in the complex plane (Rich and Jeffrey 1996).