std::cos(std::complex) (3) - Linux Manuals

std::cos(std::complex): std::cos(std::complex)

NAME

std::cos(std::complex) - std::cos(std::complex)

Synopsis

Defined in header <complex>
template< class T >
complex<T> cos( const complex<T>& z );

Computes complex cosine of a complex value z.

Parameters

z - complex value

Return value

If no errors occur, the complex cosine of z is returned.
Errors and special cases are handled as if the operation is implemented by std::cosh(i*z), where i is the imaginary unit.

Notes

The cosine is an entire function on the complex plane, and has no branch cuts.
Mathematical definition of the cosine is cos z =

eiz
+e-iz
2

Example

// Run this code

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

  int main()
  {
      std::cout << std::fixed;
      std::complex<double> z(1, 0); // behaves like real cosine along the real line
      std::cout << "cos" << z << " = " << std::cos(z)
                << " ( cos(1) = " << std::cos(1) << ")\n";

      std::complex<double> z2(0, 1); // behaves like real cosh along the imaginary line
      std::cout << "cos" << z2 << " = " << std::cos(z2)
                << " (cosh(1) = " << std::cosh(1) << ")\n";
  }

Output:

  cos(1.000000,0.000000) = (0.540302,-0.000000) ( cos(1) = 0.540302)
  cos(0.000000,1.000000) = (1.543081,-0.000000) (cosh(1) = 1.543081)