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Complex numbers in C++ | Set 2

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  • Difficulty Level : Basic
  • Last Updated : 31 Aug, 2022
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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




// 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)

Time Complexity: O(1)

Auxiliary Space: O(1)

  • 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)

CPP




// 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)

Time Complexity: O(1)

Auxiliary Space: O(1)

  • cosh() – It finds the hyperbolic 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 hyperbolic sine is:
  sinh(z)=(e^z-e^(-z))/2.
  • tanh() – It finds the hyperbolic tangent of the given complex.Mathematical function of hyperbolic tan is:
tanh(z)=(e^(2z)-1)/(e^(2z)+1)

CPP




// 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)

Time Complexity: O(1)

Auxiliary Space: O(1)

This article is contributed by Shambhavi Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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