log10

Article
07/11/2012

Returns the base 10 logarithm of a complex number.

template<class Type> 
   complex<Type> log10( 
      const complex<Type>& _ComplexNum 
   );

Parameters

_ComplexNum
The complex number whose base 10 logarithm is being determined.

Return Value

The complex number that is the base 10 logarithm of the input complex number.

Remarks

The branch cuts are along the negative real axis.

Example

// complex_log10.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 log10 of a complex number c1
   complex <double> c2 = log10 ( c1 );
   cout << "Complex number c2 = log10 ( 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; 

   // log10 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( log10 ( vc1 ) );
   complex <double> vc2  ( polar (1.0, pi / 3) );
   v1.push_back( log10 ( vc2 ) );
   complex <double> vc3  ( polar (1.0, pi / 2) );
   v1.push_back( log10 ( vc3) );
   complex <double> vc4  ( polar (1.0, 2 * pi / 3) );
   v1.push_back( log10 ( vc4 ) );
   complex <double> vc5  ( polar (1.0, 5 * pi / 6) );
   v1.push_back( log10 ( vc5 ) );
   complex <double> vc6  ( polar (1.0,  pi ) );
   v1.push_back( log10 ( vc6 ) );

   cout << "The complex components log10 (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 = log10 ( c1 ) = (0.69897,0.402719)
The modulus of c2 is: 0.806686
The argument of c2 is: 0.522706 radians, which is 29.9489 degrees.

The complex components log10 (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(0,0.227396)
(0,0.454792)
(0,0.682188)
(0,0.909584)
(0,1.13698)
(0,-1.36438)

Requirements

Header: <complex>

Namespace: std

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