log

Artículo
06/09/2015

Devuelve el logaritmo natural de un número complejo.

template<class Type> 
   complex<Type> log( 
      const complex<Type>& _ComplexNum 
   );

Parámetros

_ComplexNum
El número complejo cuyo se está determinando logaritmo natural.

Valor devuelto

El número complejo que es el logaritmo natural del número complejo de entrada.

Comentarios

Los cortes de bifurcación están a lo largo del eje real negativo.

Ejemplo

// 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;
}

Resultados del ejemplo

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)

Requisitos

complejo <deEncabezado: >

Espacio de nombres: std

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