.\" Copyright (c) 2004 Stefan Farfeleder
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.Dd August 7, 2008
.Dt CIMAG 3
.Os
.Sh NAME
.Nm cimag , cimagf , cimagl ,
.Nm conj , conjf , conjl ,
.Nm cproj , cprojf , cprojl ,
.Nm creal , crealf , creall
.Nd "functions to manipulate complex numbers"
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double
.Fn cimag "double complex z"
.Ft float
.Fn cimagf "float complex z"
.Ft "long double"
.Fn cimagl "long double complex z"
.Ft "double complex"
.Fn conj "double complex z"
.Ft "float complex"
.Fn conjf "float complex z"
.Ft "long double complex"
.Fn conjl "long double complex z"
.Ft "double complex"
.Fn cproj "double complex z"
.Ft "float complex"
.Fn cprojf "float complex z"
.Ft "long double complex"
.Fn cprojl "long double complex z"
.Ft double
.Fn creal "double complex z"
.Ft float
.Fn crealf "float complex z"
.Ft "long double"
.Fn creall "long double complex z"
.Sh DESCRIPTION
Let
.Sm off
.Fa a + b * Em i
.Sm on
denote the complex number
.Fa z .
.Pp
The
.Fn creal
functions return the real part
.Fa a ,
and the
.Fn cimag
functions return the imaginary part
.Fa b .
.Pp
The
.Fn conj
functions return the complex conjugate
.Sm off
.Fa a - b * Em i .
.Sm on
.Pp
The
.Fn cproj
functions return the projection onto the Riemann sphere.
If
.Fa z
contains an infinite component, then the result is
.Fa \*(If \*(Pm 0 Ns * Ns Em i ,
where the (zero) imaginary part of the result has the same sign as
.Fa b .
Otherwise, the result is
.Fa z .
.Pp
These functions do not signal any floating point exceptions.
.Sh STANDARDS
The
.Fn cimag ,
.Fn conj ,
.Fn cproj ,
and
.Fn creal
functions conform to
.St -isoC-99 .
.Sh HISTORY
The
.Fn cimag ,
.Fn conj
and
.Fn creal
functions first appeared in
.Fx 5.3 .
The
.Fn cproj
functions appeared in
.Fx 8.0 .