# std::acos(std::complex)

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< cpp‎ | numeric‎ | complex

Defined in header `<complex>` |  |
template< class T > complex<T> acos( const complex<T>& z ); |  | (since C++11)

Computes complex arc cosine of a complex value z. Branch cuts exist outside the interval [−1, +1] along the real axis.

### Parameters

z | - | complex value

### Return value

If no errors occur, complex arc cosine of z is returned, in the range of a strip unbounded along the imaginary axis and in the interval [0, +π] along the real axis.

### Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

- std::acos(std::conj(z)) == std::conj(std::acos(z))
- If z is `(±0,+0)`, the result is `(π/2,-0)`
- If z is `(±0,NaN)`, the result is `(π/2,NaN)`
- If z is `(x,+∞)` (for any finite x), the result is `(π/2,-∞)`
- If z is `(x,NaN)` (for any nonzero finite x), the result is `(NaN,NaN)` and FE_INVALID may be raised.
- If z is `(-∞,y)` (for any positive finite y), the result is `(π,-∞)`
- If z is `(+∞,y)` (for any positive finite y), the result is `(+0,-∞)`
- If z is `(-∞,+∞)`, the result is `(3π/4,-∞)`
- If z is `(+∞,+∞)`, the result is `(π/4,-∞)`
- If z is `(±∞,NaN)`, the result is `(NaN,±∞)` (the sign of the imaginary part is unspecified)
- If z is `(NaN,y)` (for any finite y), the result is `(NaN,NaN)` and FE_INVALID may be raised
- If z is `(NaN,+∞)`, the result is `(NaN,-∞)`
- If z is `(NaN,NaN)`, the result is `(NaN,NaN)`

### Notes

Inverse cosine (or arc cosine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞,-1) and (1,∞) of the real axis.

The mathematical definition of the principal value of arc cosine is acos z =

1
2

π + iln(iz + √1-z2
).

For any z, acos(z) = π - acos(-z).

### Example

Run this code

    #include <cmath>
    #include <complex>
    #include <iostream>

    int main()
    {
        std::cout << std::fixed;
        std::complex<double> z1(-2.0, 0.0);
        std::cout << "acos" << z1 << " = " << std::acos(z1) << '\n';

        std::complex<double> z2(-2.0, -0.0);
        std::cout << "acos" << z2 << " (the other side of the cut) = "
                  << std::acos(z2) << '\n';

        // for any z, acos(z) = pi - acos(-z)
        const double pi = std::acos(-1);
        std::complex<double> z3 = pi - std::acos(z2);
        std::cout << "cos(pi - acos" << z2 << ") = " << std::cos(z3) << '\n';
    }

Output:

    acos(-2.000000,0.000000) = (3.141593,-1.316958)
    acos(-2.000000,-0.000000) (the other side of the cut) = (3.141593,1.316958)
    cos(pi - acos(-2.000000,-0.000000)) = (2.000000,0.000000)

### See also

asin(std::complex) (C++11) | computes arc sine of a complex number (\({\small\arcsin{z} }\)arcsin(z)) (function template)
atan(std::complex) (C++11) | computes arc tangent of a complex number (\({\small\arctan{z} }\)arctan(z)) (function template)
cos(std::complex) | computes cosine of a complex number (\({\small\cos{z} }\)cos(z)) (function template)
acos acosf acosl (C++11)(C++11) | computes arc cosine (\({\small\arccos{x} }\)arccos(x)) (function)
acos(std::valarray) | applies the function std::acos to each element of valarray (function template)

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