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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CEXP 3
5.Os BSD 4
6.Sh NAME
7.Nm cexp
8.Nd complex exponential function
9.Sh SYNOPSIS
10.Fd #include <complex.h>
11.Ft double complex
12.Fn cexp "double complex z"
13.Ft long double complex
14.Fn cexpl "long double complex z"
15.Ft float complex
16.Fn cexpf "float complex z"
17.Sh DESCRIPTION
18.Fn cexp "z"
19returns the complex exponential of
20.Fa z .
21.Pp
22cexp(conj(z)) = conj(cexp(z)), for all complex floating-point numbers z.
23.Sh SPECIAL VALUES
24The conjugate symmetry of cexp() is used to abbreviate the specification of special values.
25.Pp
26.Fn cexp "�0 + 0i"
27returns 1 + 0i.
28.Pp
29.Fn cexp "x + inf i"
30returns NaN + NaN i, and raises the invalid flag, for finite
31.Fa x .
32.Pp
33.Fn cexp "x + NaN i"
34returns NaN + NaN i, for finite
35.Fa x .
36.Pp
37.Fn cexp "inf + 0i"
38returns inf + 0i.
39.Pp
40For the following two cases, cis(y) denotes cos(y) + I*sin(y).
41.Pp
42.Fn cexp "-inf + yi"
43returns 0*cis(y), for finite
44.Fa y .
45.Pp
46.Fn cexp "inf + yi"
47returns inf*cis(y), for finite nonzero
48.Fa y .
49.Pp
50.Fn cexp "-inf + inf i"
51returns -0 + 0i.
52.Pp
53.Fn cexp "inf + inf i"
54returns -inf + NaN i, and raises the invalid flag.
55.Pp
56.Fn cexp "-inf + NaN i"
57returns -0 + 0i.
58.Pp
59.Fn cexp "inf + NaN i"
60returns -inf + NaN i.
61.Pp
62.Fn cexp "NaN + 0i"
63returns NaN + 0i.
64.Pp
65.Fn cexp "NaN + yi"
66returns NaN + NaN i for all nonzero numbers y.
67.Pp
68.Fn cexp "NaN + NaN i"
69returns NaN + NaN i.
70.Pp
71.Sh SEE ALSO
72.Xr exp 3
73.Xr clog 3
74.Xr complex 3
75.Sh STANDARDS
76The
77.Fn cexp
78function conforms to ISO/IEC 9899:1999(E).