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 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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