Complex numbers in C++ | Set 2

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)