cosh
Returns the hyperbolic cosine of a complex number.
template<class Type>
complex<Type> cosh(
const complex<Type>& _ComplexNum
);
Parameters
- _ComplexNum
The complex number whose hyperbolic cosine is being determined.
Return Value
The complex number that is the hyperbolic cosine of the input complex number.
Remarks
Identities defining the complex hyperbolic cosines:
cos (z) = (1/2)*( exp (z) + exp (-z) )
cos (z) = cosh (a + bi) = cosh (a) cos (b) + isinh (a) sin (b)
Example
// complex_cosh.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>
int main( )
{
using namespace std;
double pi = 3.14159265359;
complex <double> c1 ( 3.0 , 4.0 );
cout << "Complex number c1 = " << c1 << endl;
// Values of cosine of a complex number c1
complex <double> c2 = cosh ( c1 );
cout << "Complex number c2 = cosh ( c1 ) = " << c2 << endl;
double absc2 = abs ( c2 );
double argc2 = arg ( c2 );
cout << "The modulus of c2 is: " << absc2 << endl;
cout << "The argument of c2 is: "<< argc2 << " radians, which is "
<< argc2 * 180 / pi << " degrees." << endl << endl;
// Hyperbolic cosines of the standard angles
// in the first two quadrants of the complex plane
vector <complex <double> > v1;
vector <complex <double> >::iterator Iter1;
complex <double> vc1 ( polar (1.0, pi / 6) );
v1.push_back( cosh ( vc1 ) );
complex <double> vc2 ( polar (1.0, pi / 3) );
v1.push_back( cosh ( vc2 ) );
complex <double> vc3 ( polar (1.0, pi / 2) );
v1.push_back( cosh ( vc3) );
complex <double> vc4 ( polar (1.0, 2 * pi / 3) );
v1.push_back( cosh ( vc4 ) );
complex <double> vc5 ( polar (1.0, 5 * pi / 6) );
v1.push_back( cosh ( vc5 ) );
complex <double> vc6 ( polar (1.0, pi ) );
v1.push_back( cosh ( vc6 ) );
cout << "The complex components cosh (vci), where abs (vci) = 1"
<< "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
for ( Iter1 = v1.begin( ) ; Iter1 != v1.end( ) ; Iter1++ )
cout << *Iter1 << endl;
}
Complex number c1 = (3,4) Complex number c2 = cosh ( c1 ) = (-6.58066,-7.58155) The modulus of c2 is: 10.0392 The argument of c2 is: -2.28564 radians, which is -130.957 degrees. The complex components cosh (vci), where abs (vci) = 1 & arg (vci) = i * pi / 6 of the vector v1 are: (1.22777,0.469075) (0.730543,0.39695) (0.540302,-8.70178e-014) (0.730543,-0.39695) (1.22777,-0.469075) (1.54308,2.43059e-013)
Requirements
Header: <complex>
Namespace: std