From OeisWiki
There are no approved revisions of this page, so it may
not have been
reviewed.
This article page is a stub, please help by expanding it.
The
sign function , also called the
signum function, of a
real number is defined as

This may be compactly written as

where
is the
Iverson bracket.
"Sign" of complex number
The "sign" of a
complex number z = a + b i = r e i θ =  z  e i arg(z) 
, where
is the
absolute value of a complex number and
is the
argument of a nonzero complex number (the argument of 0 being undefined), would generalize to

The "sign" of a nonzero complex number would thus give the complex number on the unit circle of the
complex plane which has the same argument as
.
If we consider the real numbers as a subset of the complex numbers, then

See also