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log

Returns the natural logarithm of a complex number.

Syntax

```
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)
```