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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CSQRT 3
5.Os BSD 4
6.Sh NAME
7.Nm csqrt
8.Nd complex square root function
9.Sh SYNOPSIS
10.Fd #include <complex.h>
11.Ft double complex
12.Fn csqrt "double complex z"
13.Ft long double complex
14.Fn csqrtl "long double complex z"
15.Ft float complex
16.Fn csqrtf "float complex z"
17.Sh DESCRIPTION
18.Fn csqrt "z"
19computes the square root of the complex floating-point number
20.Fa z ,
21with a branch cut on the negative real axis. The result is in
22the right half-plane, including the imaginary axis. For all complex
23.Fa z ,
24csqrt(conj(z)) = conj(csqrt(z)).
25.Sh SPECIAL VALUES
26The conjugate symmetry of csqrt() is used to abbreviate the specification of special values.
27.Pp
28.Fn csqrt "�0 + 0i"
29returns +0 + 0i.
30.Pp
31.Fn csqrt "x + inf i"
32returns inf + inf i for all x (including NaN).
33.Pp
34.Fn csqrt "x + NaN i"
35returns NaN + NaN i.
36.Pp
37.Fn csqrt "-inf + yi"
38returns 0 + inf i for any positively-signed finite y.
39.Pp
40.Fn csqrt "inf + yi"
41returns inf + 0i for any positively-signed finite y.
42.Pp
43.Fn csqrt "-inf + NaN i"
44returns NaN + inf i.
45.Pp
46.Fn csqrt "inf + NaN i"
47returns inf + NaN i.
48.Pp
49.Fn csqrt "NaN + yi"
50returns NaN + NaN i.
51.Pp
52.Fn csqrt "NaN + NaN i"
53returns NaN + NaN i.
54.Sh NOTES
55If
56.Fa z
57is in the upper half-plane, then
58.Fn csqrt "z"
59is in the upper-right quadrant of the complex plane.
60If
61.Fa z
62is in the lower half-plane, then
63.Fn csqrt "z"
64is in the lower-right quadrant of the complex plane.
65.Sh SEE ALSO
66.Xr complex 3
67.Sh STANDARDS
68The
69.Fn csqrt
70function conforms to ISO/IEC 9899:1999(E).