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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