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

std::sin(std::complex): std::sin(std::complex)

NAME

std::sin(std::complex) - std::sin(std::complex)

Synopsis

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

Computes complex sine of a complex value z.

Parameters

z - complex value

Return value

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

Notes

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

eiz
-e-iz
2i

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 sine along the real line
      std::cout << "sin" << z << " = " << std::sin(z)
                << " ( sin(1) = " << std::sin(1) << ")\n";

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

Output:

  sin(1.000000,0.000000) = (0.841471,0.000000) ( sin(1) = 0.841471)
  sin(0.000000,1.000000) = (0.000000,1.175201) (sinh(1) = 1.175201)