# cexp.3   [plain text]

```.\" Copyright (c) 2006 Apple Computer
.\"
.Dd October 10, 2006
.Dt CEXP 3
.Os BSD 4
.Sh NAME
.Nm cexp
.Nd complex exponential function
.Sh SYNOPSIS
.Fd #include <complex.h>
.Ft double complex
.Fn cexp "double complex z"
.Ft long double complex
.Fn cexpl "long double complex z"
.Ft float complex
.Fn cexpf "float complex z"
.Sh DESCRIPTION
.Fn cexp "z"
returns the complex exponential of
.Fa z .
.Pp
cexp(conj(z)) = conj(cexp(z)), for all complex floating-point numbers z.
.Sh SPECIAL VALUES
The conjugate symmetry of cexp() is used to abbreviate the specification of special values.
.Pp
.Fn cexp "±0 + 0i"
returns 1 + 0i.
.Pp
.Fn cexp "x + inf i"
returns NaN + NaN i, and raises the invalid flag, for finite
.Fa x .
.Pp
.Fn cexp "x + NaN i"
returns NaN + NaN i, for finite
.Fa x .
.Pp
.Fn cexp "inf + 0i"
returns inf + 0i.
.Pp
For the following two cases, cis(y) denotes cos(y) + I*sin(y).
.Pp
.Fn cexp "-inf + yi"
returns 0*cis(y), for finite
.Fa y .
.Pp
.Fn cexp "inf + yi"
returns inf*cis(y), for finite nonzero
.Fa y .
.Pp
.Fn cexp "-inf + inf i"
returns -0 + 0i.
.Pp
.Fn cexp "inf + inf i"
returns -inf + NaN i, and raises the invalid flag.
.Pp
.Fn cexp "-inf + NaN i"
returns -0 + 0i.
.Pp
.Fn cexp "inf + NaN i"
returns -inf + NaN i.
.Pp
.Fn cexp "NaN + 0i"
returns NaN + 0i.
.Pp
.Fn cexp "NaN + yi"
returns NaN + NaN i for all nonzero numbers y.
.Pp
.Fn cexp "NaN + NaN i"
returns NaN + NaN i.
.Pp