std::acos(std::complex)

 

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Technical Specifications

 

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
exp
log
log10
Power functions
pow
sqrt
Trigonometric functions
sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

 

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 [0 ; ∞) along the real axis and in the range [−iπ ; iπ] along the imaginary 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 <iostream>
#include <cmath>
#include <complex>
 
int main()
{
    std::cout << std::fixed;
    std::complex<double> z1(-2, 0);
    std::cout << "acos" << z1 << " = " << std::acos(z1) << '\n';
 
    std::complex<double> z2(-2, -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 (arcsin(z)) (function template)
atan(std::complex) (C++11)	computes arc tangent of a complex number (arctan(z)) (function template)
cos(std::complex)	computes cosine of a complex number (cos(z)) (function template)
acos	computes arc cosine (arccos(x)) (function)
acos(std::valarray)	applies the function std::acos to each element of valarray (function template)
C documentation for cacos