std::acos(std::complex)(3)

NAME
std::acos(std::complex) - std::acos(std::complex)

Synopsis
   Defined in header <complex>
   template< class T > (since C++11)
   complex<T> acos( const complex<T>& z );
   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 <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) computes arc sine of a complex number (\({\small\arcsin{z}
   (C++11) }\)arcsin(z))
                       (function template)
   atan(std::complex) computes arc tangent of a complex number (\({\small\arctan{z}
   (C++11) }\)arctan(z))
                       (function template)
   cos(std::complex) computes cosine of a complex number (\({\small\cos{z} }\)cos(z))
                       (function template)
   acos
   acosf computes arc cosine (\({\small\arccos{x} }\)arccos(x))
   acosl (function)
   (C++11)
   (C++11)
   acos(std::valarray) applies the function std::acos to each element of valarray
                       (function template)