1.\" $OpenBSD: csqrt.3,v 1.2 2013/06/05 03:40:26 tedu Exp $ 2.\" 3.\" Copyright (c) 2011 Martynas Venckus <martynas@openbsd.org> 4.\" 5.\" Permission to use, copy, modify, and distribute this software for any 6.\" purpose with or without fee is hereby granted, provided that the above 7.\" copyright notice and this permission notice appear in all copies. 8.\" 9.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16.\" 17.Dd $Mdocdate: June 5 2013 $ 18.Dt CSQRT 3 19.Os 20.Sh NAME 21.Nm csqrt , 22.Nm csqrtf , 23.Nm csqrtl 24.Nd complex square root 25.Sh SYNOPSIS 26.In complex.h 27.Ft double complex 28.Fn csqrt "double complex z" 29.Ft float complex 30.Fn csqrtf "float complex z" 31.Ft long double complex 32.Fn csqrtl "long double complex z" 33.Sh DESCRIPTION 34The 35.Fn csqrt , 36.Fn csqrtf 37and 38.Fn csqrtl 39functions compute the complex square root of 40.Fa z . 41.Pp 42If 43.Fa z 44= x + iy, then 45.Bd -literal -offset indent 46Re csqrt(z) = [ (|z| + x) / 2 ]^(1/2). 47Im csqrt(z) = [ (|z| - x) / 2 ]^(1/2). 48.Ed 49.Pp 50Note that -csqrt(z) is also a square root of 51.Fa z . 52The root chosen 53is always in the right half plane and Im csqrt(z) has the same sign 54as y. 55.Sh RETURN VALUES 56The 57.Fn csqrt , 58.Fn csqrtf 59and 60.Fn csqrtl 61functions return the complex square root of 62.Fa z . 63.Sh SEE ALSO 64.Xr cpow 3 65.Sh STANDARDS 66The 67.Fn csqrt , 68.Fn csqrtf 69and 70.Fn csqrtl 71functions conform to 72.St -isoC-99 . 73