log
Returns the natural logarithm of a complex number.
template<class Type>
complex<Type> log(
const complex<Type>& _ComplexNum
);
Parameters
- _ComplexNum
The complex number whose natural logarithm is being determined.
Return Value
The complex number that is the natural logarithm of the input complex number.
Remarks
The branch cuts are along the negative real axis.
Example
// complex_log.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 log of a complex number c1
complex <double> c2 = log ( c1 );
cout << "Complex number c2 = log ( 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;
// log 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( log ( vc1 ) );
complex <double> vc2 ( polar (1.0, pi / 3) );
v1.push_back( log ( vc2 ) );
complex <double> vc3 ( polar (1.0, pi / 2) );
v1.push_back( log ( vc3) );
complex <double> vc4 ( polar (1.0, 2 * pi / 3) );
v1.push_back( log ( vc4 ) );
complex <double> vc5 ( polar (1.0, 5 * pi / 6) );
v1.push_back( log ( vc5 ) );
complex <double> vc6 ( polar (1.0, pi ) );
v1.push_back( log ( vc6 ) );
cout << "The complex components log (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;
}
Sample Output
Complex number c1 = (3,4)
Complex number c2 = log ( c1 ) = (1.60944,0.927295)
The modulus of c2 is: 1.85746
The argument of c2 is: 0.522706 radians, which is 29.9489 degrees.
The complex components log (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(0,0.523599)
(0,1.0472)
(0,1.5708)
(0,2.0944)
(0,2.61799)
(0,-3.14159)
Requirements
Header: <complex>
Namespace: std