IMSL C# Numerical Library

Complex.Acos Method

Returns the inverse cosine (arc cosine) of a Complex, with branch cuts outside the interval [-1,1] along the real axis.

public static Complex Acos(
Complex z
);

Parameters

z: A Complex object.

Return Value

A newly constructed Complex initialized to the inverse (arc) cosine of the argument. The real part of the result is in the interval $[0,\pi]$ .

Remarks

Specifically, if z = x+iy,

$\acos(\bar{z}) = \overline{\acos(z)}$ .

$\acos(\pm 0 + i0)$ returns $\pi/2 - i0$ .

$\acos(-\infty + i\infty)$ returns $3 \pi/4 - i\infty$ .

$\acos(+\infty + i\infty)$ returns $\pi/4 - i\infty$ .

$\acos(x + i\infty )$ returns $\pi/2 - i\infty$ , for finite x.

$\acos(-\infty + iy)$ returns $\pi- i\infty$ , for positive-signed finite y.

$\acos(+\infty + iy)$ returns $+0 - i\infty$ , for positive-signed finite y.

$\acos(\pm \infty + i\NaN)$ returns $\NaN \pm i\infty$ (where the sign of the imaginary part of the result is unspecified).

$\acos(\pm 0 + i\NaN)$ returns $\pi/2 + i\NaN$ .

$\acos(\NaN + i\infty)$ returns $\NaN - i\infty$ .

$\acos(x + i\NaN)$ returns $\NaN + i\NaN$ , for nonzero finite x.

$\acos(\NaN + iy)$ returns $\NaN + i\NaN$ , for finite y.

$\acos(\NaN + i\NaN)$ returns $\NaN + i\NaN$ .

See Also

Complex Class | Imsl.Math Namespace