# std::sin(std::complex)

< cpp‎ | numeric‎ | complex

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

Computes complex sine of a complex value z.

## Contents

### 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

#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)