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Complex numbers in C++ | Set 2

  • Difficulty Level : Basic
  • Last Updated : 06 Jul, 2017

We introduced and discussed the concept in Complex numbers in C++ | Set 1

The remaining functions with example are discussed here:

  • log() – It is used to return the log of the complex number.




    // CPP program to illustrate the use of log()
    #include <iostream>     
       
    // for std::complex, std::log
    #include <complex> 
    using namespace std;
       
    // driver program
    int main ()
    {    
      // initializing the complex: (-1.0+0.0i)
      complex<double> mycomplex (-1.0, 0.0);
       
      // use of log()
      cout << "The log of " << mycomplex << " is "
           << log(mycomplex) <<endl;
       
      return 0;

    Output:

    The log of (-1,0) is (0,3.14159)
    
  • cos() – It computes complex cosine of a complex value z. Mathematical definition of the cosine is
    cos z = (e^(iz) + e^(-iz))/2
  • sin() – It computes the complex sine of a complex value z. Mathematical definition of the cosine is
     sin z = (e^(iz) - e^(-iz))/2i
  • tan() – It computes the complex tangent of a complex value z. Mathematical definition of the tangent is
    tan z = i(e^(-iz) - e^(iz)) / (e^(-iz) + e^iz)




    // example to illustrate the use of sin(), cos() and tan()
    #include <iostream>     
       
    // CPP program to illustrate
    // std::complex, std::cos, std::sin, std::tan
    #include <complex> 
    using namespace std;
       
    // driver program
    int main ()
    {    
      // initializing the complex: (-1.0+0.0i)
      complex<double> mycomplex (0.0, 1.0);
       
      // use of cos()
      cout << "The cos of " << mycomplex << " is "
           << cos(mycomplex) <<endl;
             
      // use of sin()
      cout << "The sin of " << mycomplex << " is "
           << sin(mycomplex) <<endl; 
             
      // use of tan()
      cout << "The tan of " << mycomplex << " is "
           << tan(mycomplex) <<endl; 
       
      return 0;
    }

    Output:

    The cos of (0,1) is (1.54308,-0)
    The sin of (0,1) is (0,1.1752)
    The tan of (0,1) is (0,0.761594)
    
  • cosh() – It finds the hyperolic cosine of the given complex. Mathematical function of hyperbolic cosine is:
    cosh(z)=(e^z+e^(-z))/2
  • sinh() – It finds the hyperbolic sine of the given complex. Mathematical function of hyperolic sine is:
      sinh(z)=(e^z-e^(-z))/2.
  • tanh() – It finds the hyperbolic tangent of the given complex.Mathematical function of hyperolic tan is:
    tanh(z)=(e^(2z)-1)/(e^(2z)+1)




    // CPP program to illustrate the 
    // use of cosh(),sinh(),tanh()
    #include <iostream>
    #include <cmath>
      
    // For std::complex
    #include <complex>
    using namespace std;
       
    // Driver program
    int main()
    {       
        // behaves like real cosh, sinh, tanh along the real line;
        // z = a + 0i
        complex<double> z(1, 0); 
        cout << "cosh" << z << " = " << cosh(z)
                  << " (cosh(1) = " << cosh(1) << ")"<<endl;
        cout << "sinh" << z << " = " << sinh(z)
                  << " (sinh(1) = " << sinh(1) << ")"<<endl;
        cout << "tanh" << z << " = " << tanh(z)
                  << " (tanh(1) = " << tanh(1) << ")"<<endl;
          
        // behaves like real cosine,sine,tangent along the imaginary line; z2=0+1i
        complex<double> z2(0, 1); 
        cout << "cosh" << z2 << " = " << cosh(z2)
                  << " ( cos(1) = " << cos(1) << ")"<<endl;
        cout << "sinh" << z2 << " = " << sinh(z2)
                  << " ( sin(1) = " << sin(1) << ")"<<endl;
        cout << "tanh" << z2 << " = " << tanh(z2)
                  << " ( tan(1) = " << tan(1) << ")"<<endl;
    }

    Output:

    cosh(1.000000,0.000000) = (1.543081,0.000000) (cosh(1) = 1.543081)
    sinh(1.000000,0.000000) = (1.175201,0.000000) (sinh(1) = 1.175201)
    tanh(1.000000,0.000000) = (0.761594,0.000000) (tanh(1) = 0.761594)
    cosh(0.000000,1.000000) = (0.540302,0.000000) ( cos(1) = 0.540302)
    sinh(0.000000,1.000000) = (0.000000,0.841471) ( sin(1) = 0.841471)
    tanh(0.000000,1.000000) = (0.000000,1.557408) ( tan(1) = 1.557408)
    

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